Theorem aistbisfiaxb 41086

Description: Given a is equivalent to T., Given b is equivalent to F. there exists a proof for a-xor-b. (Contributed by Jarvin Udandy, 31-Aug-2016.)

Hypotheses

Ref	Expression
aistbisfiaxb.1	|- ( ph <-> T. )
aistbisfiaxb.2	|- ( ps <-> F. )

Assertion

Ref	Expression
aistbisfiaxb	|- ( ph \/_ ps )

Proof of Theorem aistbisfiaxb

Step	Hyp	Ref	Expression
1		aistbisfiaxb.1	. . 3 |- ( ph <-> T. )
2	1	aistia 41064	. 2 |- ph
3		aistbisfiaxb.2	. . 3 |- ( ps <-> F. )
4	3	aisfina 41065	. 2 |- -. ps
5	2, 4	abnotbtaxb 41082	1 |- ( ph \/_ ps )

Syntax hints:   <-> wb 196   \/_ wxo 1464   T. wtru 1484   F. wfal 1488

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-an 386  df-xor 1465  df-tru 1486  df-fal 1489

This theorem is referenced by: (None)