Theorem pm2.61iii 179

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 25	. . 3 |- ( ph -> ( -. ch -> th ) )
5		pm2.61iii.3	. . . 4 |- ( ps -> th )
6	5	a1d 25	. . 3 |- ( ps -> ( -. ch -> th ) )
7	2, 4, 6	pm2.61ii 177	. 2 |- ( -. ch -> th )
8	1, 7	pm2.61i 176	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:  axrepnd  9416  axacndlem4  9432  axacndlem5  9433  axacnd  9434