Theorem nic-mpALT 1085

Description: A direct proof of nic-mp 1084.

Hypotheses

Ref	Expression
nic-jmin	|- ph
nic-jmaj	|- (ph -/\ (ch -/\ ps))

Assertion

Ref	Expression
nic-mpALT	|- ps

Proof of Theorem nic-mpALT

Step	Hyp	Ref	Expression
1		nic-jmin	. 2 |- ph
2		nic-jmaj	. . . . 5 |- (ph -/\ (ch -/\ ps))
3		df-nand 1077	. . . . . 6 |- ((ph -/\ (ch -/\ ps)) <-> -. (ph /\ (ch -/\ ps)))
4		df-nand 1077	. . . . . . . 8 |- ((ch -/\ ps) <-> -. (ch /\ ps))
5	4	anbi2i 535	. . . . . . 7 |- ((ph /\ (ch -/\ ps)) <-> (ph /\ -. (ch /\ ps)))
6	5	notbii 203	. . . . . 6 |- (-. (ph /\ (ch -/\ ps)) <-> -. (ph /\ -. (ch /\ ps)))
7	3, 6	bitri 189	. . . . 5 |- ((ph -/\ (ch -/\ ps)) <-> -. (ph /\ -. (ch /\ ps)))
8	2, 7	mpbi 205	. . . 4 |- -. (ph /\ -. (ch /\ ps))
9		iman 254	. . . 4 |- ((ph -> (ch /\ ps)) <-> -. (ph /\ -. (ch /\ ps)))
10	8, 9	mpbir 206	. . 3 |- (ph -> (ch /\ ps))
11	10	pm3.27d 350	. 2 |- (ph -> ps)
12	1, 11	ax-mp 7	1 |- ps

Syntax hints:  -. wn 2   -> wi 3   /\ wa 239   -/\ wnand 1076

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 163  df-an 241  df-nand 1077

Copyright terms: Public domain