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Theorem xorcom 1324
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 682 . . 3 ((𝜑𝜓) ↔ (𝜓𝜑))
2 ancom 262 . . . 4 ((𝜑𝜓) ↔ (𝜓𝜑))
32notbii 629 . . 3 (¬ (𝜑𝜓) ↔ ¬ (𝜓𝜑))
41, 3anbi12i 448 . 2 (((𝜑𝜓) ∧ ¬ (𝜑𝜓)) ↔ ((𝜓𝜑) ∧ ¬ (𝜓𝜑)))
5 df-xor 1312 . 2 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))
6 df-xor 1312 . 2 ((𝜓𝜑) ↔ ((𝜓𝜑) ∧ ¬ (𝜓𝜑)))
74, 5, 63bitr4i 210 1 ((𝜑𝜓) ↔ (𝜓𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wa 102  wb 103  wo 664  wxo 1311
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665
This theorem depends on definitions:  df-bi 115  df-xor 1312
This theorem is referenced by:  rpnegap  9135
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