Theorem mpto2OLD 1535

Description: Obsolete version of mpto2 1534 as of 12-Nov-2017. (Contributed by David A. Wheeler, 3-Jul-2016.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
mpto2OLD.1	|- ph
mpto2OLD.2	|- (ph \/_ ps)

Assertion

Ref	Expression
mpto2OLD	|- -. ps

Proof of Theorem mpto2OLD

Step	Hyp	Ref	Expression
1		mpto2OLD.1	. 2 |- ph
2		mpto2OLD.2	. . . . 5 |- (ph \/_ ps)
3		df-xor 1305	. . . . 5 |- ((ph \/_ ps) <-> -. (ph <-> ps))
4	2, 3	mpbi 199	. . . 4 |- -. (ph <-> ps)
5		nbbn 347	. . . 4 |- ((-. ph <-> ps) <-> -. (ph <-> ps))
6	4, 5	mpbir 200	. . 3 |- (-. ph <-> ps)
7	6	con1bii 321	. 2 |- (-. ps <-> ph)
8	1, 7	mpbir 200	1 |- -. ps

Syntax hints:  -. wn 3   <-> wb 176   \/_ wxo 1304

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 177  df-xor 1305

This theorem is referenced by: (None)