Theorem aisbnaxb 41078

Description: Given a is equivalent to b, there exists a proof for (not (a xor b)). (Contributed by Jarvin Udandy, 28-Aug-2016.)

Hypothesis

Ref	Expression
aisbnaxb.1	|- ( ph <-> ps )

Assertion

Ref	Expression
aisbnaxb	|- -. ( ph \/_ ps )

Proof of Theorem aisbnaxb

Step	Hyp	Ref	Expression
1		aisbnaxb.1	. . 3 |- ( ph <-> ps )
2	1	notnoti 137	. 2 |- -. -. ( ph <-> ps )
3		df-xor 1465	. 2 |- ( ( ph \/_ ps ) <-> -. ( ph <-> ps ) )
4	2, 3	mtbir 313	1 |- -. ( ph \/_ ps )

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:  dandysum2p2e4  41165