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  318  ancr  321  anc2r  328  pm2.65  665  pm2.18dc  862  con4biddc  864  hbim1  1618  sbcof2  1858  ralimia  2593  ceqsalg  2831  rspct  2903  elabgt  2947  fvmptt  5738  ordiso2  7233  bj-exlimmp  16365  bj-rspgt  16382  bj-indint  16526