diff --git a/java/ql/lib/semmle/code/java/controlflow/internal/GuardsLogic.qll b/java/ql/lib/semmle/code/java/controlflow/internal/GuardsLogic.qll
index 7c4d49c90c7a..269a626c7851 100644
--- a/java/ql/lib/semmle/code/java/controlflow/internal/GuardsLogic.qll
+++ b/java/ql/lib/semmle/code/java/controlflow/internal/GuardsLogic.qll
@@ -23,19 +23,23 @@ predicate implies_v1(Guard g1, boolean b1, Guard g2, boolean b2) {
   or
   g1.(OrBitwiseExpr).getAnOperand() = g2 and b1 = false and b2 = false
   or
+  g1.(AssignAndExpr).getSource() = g2 and b1 = true and b2 = true
+  or
+  g1.(AssignOrExpr).getSource() = g2 and b1 = false and b2 = false
+  or
   g1.(AndLogicalExpr).getAnOperand() = g2 and b1 = true and b2 = true
   or
   g1.(OrLogicalExpr).getAnOperand() = g2 and b1 = false and b2 = false
   or
   g1.(LogNotExpr).getExpr() = g2 and
   b1 = b2.booleanNot() and
-  (b1 = true or b1 = false)
+  b1 = [true, false]
   or
   exists(EqualityTest eqtest, boolean polarity, BooleanLiteral boollit |
     eqtest = g1 and
     eqtest.hasOperands(g2, boollit) and
     eqtest.polarity() = polarity and
-    (b1 = true or b1 = false) and
+    b1 = [true, false] and
     b2 = b1.booleanXor(polarity).booleanXor(boollit.getBooleanValue())
   )
   or
@@ -56,16 +60,20 @@ predicate implies_v1(Guard g1, boolean b1, Guard g2, boolean b2) {
   exists(MethodAccess check | check = g1 |
     conditionCheck(check, _) and
     g2 = check.getArgument(0) and
-    (b1 = true or b1 = false) and
+    b1 = [true, false] and
     b2 = b1
   )
   or
   exists(BaseSsaUpdate vbool |
+    vbool.getDefiningExpr().(VariableAssign).getSource() = g2 or
+    vbool.getDefiningExpr().(AssignOp) = g2
+  |
     vbool.getAUse() = g1 and
-    vbool.getDefiningExpr().(VariableAssign).getSource() = g2 and
-    (b1 = true or b1 = false) and
+    b1 = [true, false] and
     b2 = b1
   )
+  or
+  g1.(AssignExpr).getSource() = g2 and b2 = b1 and b1 = [true, false]
 }
 
 /**
@@ -79,9 +87,11 @@ predicate implies_v2(Guard g1, boolean b1, Guard g2, boolean b2) {
   implies_v1(g1, b1, g2, b2)
   or
   exists(SsaExplicitUpdate vbool |
+    vbool.getDefiningExpr().(VariableAssign).getSource() = g2 or
+    vbool.getDefiningExpr().(AssignOp) = g2
+  |
     vbool.getAUse() = g1 and
-    vbool.getDefiningExpr().(VariableAssign).getSource() = g2 and
-    (b1 = true or b1 = false) and
+    b1 = [true, false] and
     b2 = b1
   )
   or
diff --git a/java/ql/test/query-tests/Nullness/B.java b/java/ql/test/query-tests/Nullness/B.java
index 193d61e497f1..0ab6d58dbaeb 100644
--- a/java/ql/test/query-tests/Nullness/B.java
+++ b/java/ql/test/query-tests/Nullness/B.java
@@ -371,4 +371,41 @@ public void corrConds5(Object y, Object z) {
     }
   }
 
+  public void bitwise(Object x, boolean b) {
+    boolean notnull = x != null;
+
+    boolean g1 = notnull;
+    g1 &= b;
+    if (g1) {
+      x.hashCode(); // OK
+    }
+
+    boolean g2 = b;
+    g2 &= notnull;
+    if (g2) {
+      x.hashCode(); // OK
+    }
+
+    boolean g3 = !notnull;
+    g3 |= b;
+    if (!g3) {
+      x.hashCode(); // OK
+    }
+
+    boolean g4 = b;
+    g4 |= !notnull;
+    if (!g4) {
+      x.hashCode(); // OK
+    }
+
+    boolean g5 = g1 = b & notnull;
+    if (g5) {
+      x.hashCode(); // OK
+    }
+
+    g5 |= b;
+    if (g5) {
+      x.hashCode(); // NPE
+    }
+  }
 }
diff --git a/java/ql/test/query-tests/Nullness/NullMaybe.expected b/java/ql/test/query-tests/Nullness/NullMaybe.expected
index 8f72be0619f9..5dfcc72f1d41 100644
--- a/java/ql/test/query-tests/Nullness/NullMaybe.expected
+++ b/java/ql/test/query-tests/Nullness/NullMaybe.expected
@@ -17,6 +17,7 @@
 | B.java:190:7:190:7 | o | Variable $@ may be null here because of $@ assignment. | B.java:178:5:178:20 | Object o | o | B.java:186:5:186:12 | ...=... | this |
 | B.java:279:7:279:7 | a | Variable $@ may be null here because of $@ assignment. | B.java:276:5:276:19 | int[] a | a | B.java:276:11:276:18 | a | this |
 | B.java:292:7:292:7 | b | Variable $@ may be null here because of $@ assignment. | B.java:287:5:287:44 | int[] b | b | B.java:287:11:287:43 | b | this |
+| B.java:408:7:408:7 | x | Variable $@ may be null here as suggested by $@ null guard. | B.java:374:23:374:30 | x | x | B.java:375:23:375:31 | ... != ... | this |
 | C.java:9:44:9:45 | a2 | Variable $@ may be null here as suggested by $@ null guard. | C.java:6:5:6:23 | long[][] a2 | a2 | C.java:7:34:7:54 | ... != ... | this |
 | C.java:9:44:9:45 | a2 | Variable $@ may be null here because of $@ assignment. | C.java:6:5:6:23 | long[][] a2 | a2 | C.java:6:14:6:22 | a2 | this |
 | C.java:10:17:10:18 | a3 | Variable $@ may be null here as suggested by $@ null guard. | C.java:8:5:8:21 | long[] a3 | a3 | C.java:9:38:9:58 | ... != ... | this |