Theorem nic-mpALT 1597

Description: A direct proof of nic-mp 1596. (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 1448	. . . . . 6 |- ( ( ph -/\ ( ch -/\ ps ) ) <-> -. ( ph /\ ( ch -/\ ps ) ) )
4		df-nan 1448	. . . . . . 7 |- ( ( ch -/\ ps ) <-> -. ( ch /\ ps ) )
5	4	anbi2i 730	. . . . . 6 |- ( ( ph /\ ( ch -/\ ps ) ) <-> ( ph /\ -. ( ch /\ ps ) ) )
6	3, 5	xchbinx 324	. . . . 5 |- ( ( ph -/\ ( ch -/\ ps ) ) <-> -. ( ph /\ -. ( ch /\ ps ) ) )
7	2, 6	mpbi 220	. . . 4 |- -. ( ph /\ -. ( ch /\ ps ) )
8		iman 440	. . . 4 |- ( ( ph -> ( ch /\ ps ) ) <-> -. ( ph /\ -. ( ch /\ ps ) ) )
9	7, 8	mpbir 221	. . 3 |- ( ph -> ( ch /\ ps ) )
10	9	simprd 479	. 2 |- ( ph -> ps )
11	1, 10	ax-mp 5	1 |- ps

Syntax hints:   -. wn 3   -> wi 4   /\ wa 384   -/\ wnan 1447

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-an 386  df-nan 1448

This theorem is referenced by: (None)