Theorem pm2.61iii 132

Description: Inference eliminating three antecedents.

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.2	. . . . 5 |- (ph -> th)
2	1	a1d 12	. . . 4 |- (ph -> (-. ch -> th))
3	2	a1d 12	. . 3 |- (ph -> (-. ps -> (-. ch -> th)))
4		pm2.61iii.1	. . 3 |- (-. ph -> (-. ps -> (-. ch -> th)))
5	3, 4	pm2.61i 126	. 2 |- (-. ps -> (-. ch -> th))
6		pm2.61iii.3	. 2 |- (ps -> th)
7		pm2.61iii.4	. 2 |- (ch -> th)
8	5, 6, 7	pm2.61ii 130	1 |- th

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  axrepnd 4869  axacndlem4 4885  axacndlem5 4886  axacnd 4887

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

Copyright terms: Public domain