Theorem xornbi 1277

Description: A consequence of exclusive or. For decidable propositions this is an equivalence, as seen at xornbidc 1282. (Contributed by Jim Kingdon, 10-Mar-2018.)

Assertion

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

Proof of Theorem xornbi

Step	Hyp	Ref	Expression
1		xorbin 1275	. 2 |- ( ( ph \/_ ps ) -> ( ph <-> -. ps ) )
2		pm5.18im 1276	. . 3 |- ( ( ph <-> ps ) -> -. ( ph <-> -. ps ) )
3	2	con2i 557	. 2 |- ( ( ph <-> -. ps ) -> -. ( ph <-> ps ) )
4	1, 3	syl 14	1 |- ( ( ph \/_ ps ) -> -. ( ph <-> ps ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 98   \/_ wxo 1266

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630

This theorem depends on definitions:  df-bi 110  df-xor 1267

This theorem is referenced by: (None)