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Theorem xorcom 1276
Description: is commutative. (Contributed by David A. Wheeler, 6-Oct-2018.)
Assertion
Ref Expression
xorcom ((φψ) ↔ (ψφ))

Proof of Theorem xorcom
StepHypRef Expression
1 orcom 646 . . 3 ((φ ψ) ↔ (ψ φ))
2 ancom 253 . . . 4 ((φ ψ) ↔ (ψ φ))
32notbii 593 . . 3 (¬ (φ ψ) ↔ ¬ (ψ φ))
41, 3anbi12i 433 . 2 (((φ ψ) ¬ (φ ψ)) ↔ ((ψ φ) ¬ (ψ φ)))
5 df-xor 1266 . 2 ((φψ) ↔ ((φ ψ) ¬ (φ ψ)))
6 df-xor 1266 . 2 ((ψφ) ↔ ((ψ φ) ¬ (ψ φ)))
74, 5, 63bitr4i 201 1 ((φψ) ↔ (ψφ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   wa 97  wb 98   wo 628  wxo 1265
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110  df-xor 1266
This theorem is referenced by:  rpnegap  8350
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