Theorem abnotataxb 41083

Description: Assuming not a, b, there exists a proof a-xor-b.) (Contributed by Jarvin Udandy, 31-Aug-2016.)

Hypotheses

Ref	Expression
abnotataxb.1	|- -. ph
abnotataxb.2	|- ps

Assertion

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

Proof of Theorem abnotataxb

Step	Hyp	Ref	Expression
1		abnotataxb.2	. . . . 5 |- ps
2		abnotataxb.1	. . . . 5 |- -. ph
3	1, 2	pm3.2i 471	. . . 4 |- ( ps /\ -. ph )
4	3	olci 406	. . 3 |- ( ( ph /\ -. ps ) \/ ( ps /\ -. ph ) )
5		xor 935	. . 3 |- ( -. ( ph <-> ps ) <-> ( ( ph /\ -. ps ) \/ ( ps /\ -. ph ) ) )
6	4, 5	mpbir 221	. 2 |- -. ( ph <-> ps )
7		df-xor 1465	. 2 |- ( ( ph \/_ ps ) <-> -. ( ph <-> ps ) )
8	6, 7	mpbir 221	1 |- ( ph \/_ ps )

Syntax hints:   -. wn 3   <-> wb 196   \/ wo 383   /\ wa 384   \/_ 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-or 385  df-an 386  df-xor 1465

This theorem is referenced by:  aisfbistiaxb  41087