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Theorem xorcom 1349
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 700 . . 3 ((𝜑𝜓) ↔ (𝜓𝜑))
2 ancom 264 . . . 4 ((𝜑𝜓) ↔ (𝜓𝜑))
32notbii 640 . . 3 (¬ (𝜑𝜓) ↔ ¬ (𝜓𝜑))
41, 3anbi12i 453 . 2 (((𝜑𝜓) ∧ ¬ (𝜑𝜓)) ↔ ((𝜓𝜑) ∧ ¬ (𝜓𝜑)))
5 df-xor 1337 . 2 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))
6 df-xor 1337 . 2 ((𝜓𝜑) ↔ ((𝜓𝜑) ∧ ¬ (𝜓𝜑)))
74, 5, 63bitr4i 211 1 ((𝜑𝜓) ↔ (𝜓𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wa 103  wb 104  wo 680  wxo 1336
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681
This theorem depends on definitions:  df-bi 116  df-xor 1337
This theorem is referenced by:  rpnegap  9425
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