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Theorem xorcom 1636
Description: The connector is commutative. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
xorcom ((𝜑𝜓) ↔ (𝜓𝜑))

Proof of Theorem xorcom
StepHypRef Expression
1 bicom 213 . . 3 ((𝜑𝜓) ↔ (𝜓𝜑))
21notbii 311 . 2 (¬ (𝜑𝜓) ↔ ¬ (𝜓𝜑))
3 df-xor 1634 . 2 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
4 df-xor 1634 . 2 ((𝜓𝜑) ↔ ¬ (𝜓𝜑))
52, 3, 43bitr4i 294 1 ((𝜑𝜓) ↔ (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 197  wxo 1633
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 198  df-xor 1634
This theorem is referenced by:  xorneg1  1644  falxortru  1700  hadcoma  1708  hadcomb  1709  cadcoma  1721
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