Theorem aisfbistiaxb 41087

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

Hypotheses

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

Assertion

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

Proof of Theorem aisfbistiaxb

Step	Hyp	Ref	Expression
1		aisfbistiaxb.1	. . 3 |- ( ph <-> F. )
2	1	aisfina 41065	. 2 |- -. ph
3		aisfbistiaxb.2	. . 3 |- ( ps <-> T. )
4	3	aistia 41064	. 2 |- ps
5	2, 4	abnotataxb 41083	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-or 385  df-an 386  df-xor 1465  df-tru 1486  df-fal 1489

This theorem is referenced by: (None)