Theorem a2i 11

Description: Inference derived from axiom ax-2 7. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
a2i.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
a2i	|- ( ( ph -> ps ) -> ( ph -> ch ) )

Proof of Theorem a2i

Step	Hyp	Ref	Expression
1		a2i.1	. 2 |- ( ph -> ( ps -> ch ) )
2		ax-2 7	. 2 |- ( ( ph -> ( ps -> ch ) ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ph -> ps ) -> ( ph -> ch ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  imim2i  12  mpd  13  sylcom  28  pm2.43  53  ancl  316  ancr  319  anc2r  326  pm2.65  648  pm2.18dc  840  con4biddc  842  hbim1  1549  sbcof2  1782  ralimia  2493  ceqsalg  2714  rspct  2782  elabgt  2825  fvmptt  5512  ordiso2  6920  bj-exlimmp  12976  bj-rspgt  12993  bj-indint  13129