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Theorem xorcom 1307
Description: is commutative. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
xorcom ((φψ) ↔ (ψφ))

Proof of Theorem xorcom
StepHypRef Expression
1 bicom 191 . . 3 ((φψ) ↔ (ψφ))
21notbii 287 . 2 (¬ (φψ) ↔ ¬ (ψφ))
3 df-xor 1305 . 2 ((φψ) ↔ ¬ (φψ))
4 df-xor 1305 . 2 ((ψφ) ↔ ¬ (ψφ))
52, 3, 43bitr4i 268 1 ((φψ) ↔ (ψφ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176  wxo 1304
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 177  df-xor 1305
This theorem is referenced by:  xorneg2  1312  hadcoma  1388  hadcomb  1389  cadcoma  1395
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