Theorem mtp-xorOLD 1537

Description: Obsolete version of mtp-xor 1536 as of 11-Nov-2017. (Contributed by David A. Wheeler, 4-Jul-2016.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
mtp-xorOLD	|- ps

Proof of Theorem mtp-xorOLD

Step	Hyp	Ref	Expression
1		mtp-xor.1	. 2 |- -. ph
2		mtp-xor.2	. . . . 5 |- (ph \/_ ps)
3		df-xor 1305	. . . . 5 |- ((ph \/_ ps) <-> -. (ph <-> ps))
4	2, 3	mpbi 199	. . . 4 |- -. (ph <-> ps)
5		bicom 191	. . . 4 |- ((ph <-> ps) <-> (ps <-> ph))
6	4, 5	mtbi 289	. . 3 |- -. (ps <-> ph)
7		xor3 346	. . 3 |- (-. (ps <-> ph) <-> (ps <-> -. ph))
8	6, 7	mpbi 199	. 2 |- (ps <-> -. ph)
9	1, 8	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)