Theorem pm2.61iii 159

Description: Inference eliminating three antecedents. (Contributed by NM, 2-Jan-2002.) (Proof shortened by Wolf Lammen, 22-Sep-2013.)

Hypotheses

Ref	Expression
pm2.61iii.1	|- (-. ph -> (-. ps -> (-. ch -> th)))
pm2.61iii.2	|- (ph -> th)
pm2.61iii.3	|- (ps -> th)
pm2.61iii.4	|- (ch -> th)

Assertion

Ref	Expression
pm2.61iii	|- th

Proof of Theorem pm2.61iii

Step	Hyp	Ref	Expression
1		pm2.61iii.4	. 2 |- (ch -> th)
2		pm2.61iii.1	. . 3 |- (-. ph -> (-. ps -> (-. ch -> th)))
3		pm2.61iii.2	. . . 4 |- (ph -> th)
4	3	a1d 22	. . 3 |- (ph -> (-. ch -> th))
5		pm2.61iii.3	. . . 4 |- (ps -> th)
6	5	a1d 22	. . 3 |- (ps -> (-. ch -> th))
7	2, 4, 6	pm2.61ii 157	. 2 |- (-. ch -> th)
8	1, 7	pm2.61i 156	1 |- th

Syntax hints:  -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by: (None)