Theorem pm2.61nii 131

Description: Inference eliminating two antecedents.

Hypotheses

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

Assertion

Ref	Expression
pm2.61nii	|- ch

Proof of Theorem pm2.61nii

Step	Hyp	Ref	Expression
1		pm2.61nii.1	. . . 4 |- (ph -> (ps -> ch))
2	1	com12 11	. . 3 |- (ps -> (ph -> ch))
3		pm2.61nii.2	. . 3 |- (-. ph -> ch)
4	2, 3	pm2.61d1 128	. 2 |- (ps -> ch)
5		pm2.61nii.3	. 2 |- (-. ps -> ch)
6	4, 5	pm2.61i 126	1 |- ch

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  ecase 753  3ecase 923  prex 2781

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

Copyright terms: Public domain