Theorem pm2.61iii 114

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 14	. . . 4 |- (ph -> (-. ch -> th))
3	2	a1d 14	. . 3 |- (ph -> (-. ps -> (-. ch -> th)))
4		pm2.61iii.1	. . 3 |- (-. ph -> (-. ps -> (-. ch -> th)))
5	3, 4	pm2.61i 110	. 2 |- (-. ps -> (-. ch -> th))
6		pm2.61iii.3	. 2 |- (ps -> th)
7		pm2.61iii.4	. 2 |- (ch -> th)
8	5, 6, 7	pm2.61ii 113	1 |- th

Syntax hints:  -. wn 1   -> wi 2

This theorem is referenced by:  axrepnd 3740  axacndlem4 3756  axacndlem5 3757  axacnd 3758

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

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