Theorem pm2.61nii 178

Description: Inference eliminating two antecedents. (Contributed by NM, 13-Jul-2005.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 13-Nov-2012.)

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	. . 3 |- ( ph -> ( ps -> ch ) )
2		pm2.61nii.3	. . 3 |- ( -. ps -> ch )
3	1, 2	pm2.61d1 171	. 2 |- ( ph -> ch )
4		pm2.61nii.2	. 2 |- ( -. ph -> ch )
5	3, 4	pm2.61i 176	1 |- ch

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:  ecase  983  3ecase  1437  prex  4909  nbgr0vtxlem  26251