Theorem nic-mpALT 1437

Description: A direct proof of nic-mp 1436. (Contributed by NM, 30-Dec-2008.) (Proof modification is discouraged.) (New usage is discouraged.)

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-nan 1288	. . . . . 6 |- ((ph -/\ (ch -/\ ps)) <-> -. (ph /\ (ch -/\ ps)))
4		df-nan 1288	. . . . . . 7 |- ((ch -/\ ps) <-> -. (ch /\ ps))
5	4	anbi2i 675	. . . . . 6 |- ((ph /\ (ch -/\ ps)) <-> (ph /\ -. (ch /\ ps)))
6	3, 5	xchbinx 301	. . . . 5 |- ((ph -/\ (ch -/\ ps)) <-> -. (ph /\ -. (ch /\ ps)))
7	2, 6	mpbi 199	. . . 4 |- -. (ph /\ -. (ch /\ ps))
8		iman 413	. . . 4 |- ((ph -> (ch /\ ps)) <-> -. (ph /\ -. (ch /\ ps)))
9	7, 8	mpbir 200	. . 3 |- (ph -> (ch /\ ps))
10	9	simprd 449	. 2 |- (ph -> ps)
11	1, 10	ax-mp 5	1 |- ps

Syntax hints:  -. wn 3   -> wi 4   /\ wa 358   -/\ wnan 1287

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-an 360  df-nan 1288

This theorem is referenced by: (None)