Theorem xorcom 1467

Description: The connector \/_ is commutative. (Contributed by Mario Carneiro, 4-Sep-2016.)

Assertion

Ref	Expression
xorcom	|- ( ( ph \/_ ps ) <-> ( ps \/_ ph ) )

Proof of Theorem xorcom

Step	Hyp	Ref	Expression
1		bicom 212	. . 3 |- ( ( ph <-> ps ) <-> ( ps <-> ph ) )
2	1	notbii 310	. 2 |- ( -. ( ph <-> ps ) <-> -. ( ps <-> ph ) )
3		df-xor 1465	. 2 |- ( ( ph \/_ ps ) <-> -. ( ph <-> ps ) )
4		df-xor 1465	. 2 |- ( ( ps \/_ ph ) <-> -. ( ps <-> ph ) )
5	2, 3, 4	3bitr4i 292	1 |- ( ( ph \/_ ps ) <-> ( ps \/_ ph ) )

Syntax hints:   -. wn 3   <-> wb 196   \/_ wxo 1464

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 197  df-xor 1465

This theorem is referenced by:  xorneg1  1475  falxortru  1530  hadcoma  1538  hadcomb  1539  cadcoma  1551