Theorem pm2.86i 98

Description: Inference based on pm2.86 100. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 3-Apr-2013.)

Hypothesis

Ref	Expression
pm2.86i.1	|- ( ( ph -> ps ) -> ( ph -> ch ) )

Assertion

Ref	Expression
pm2.86i	|- ( ph -> ( ps -> ch ) )

Proof of Theorem pm2.86i

Step	Hyp	Ref	Expression
1		ax-1 6	. . 3 |- ( ps -> ( ph -> ps ) )
2		pm2.86i.1	. . 3 |- ( ( ph -> ps ) -> ( ph -> ch ) )
3	1, 2	syl 14	. 2 |- ( ps -> ( ph -> ch ) )
4	3	com12 30	1 |- ( ph -> ( ps -> ch ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  nfrimi  1513  cbv1  1733  cbv1v  1735