Theorem mpd3an3 1233

Description: An inference based on modus ponens. (Contributed by NM, 8-Nov-2007.)

Hypotheses

Ref	Expression
mpd3an3.2	|- ( ( ph /\ ps ) -> ch )
mpd3an3.3	|- ( ( ph /\ ps /\ ch ) -> th )

Assertion

Ref	Expression
mpd3an3	|- ( ( ph /\ ps ) -> th )

Proof of Theorem mpd3an3

Step	Hyp	Ref	Expression
1		mpd3an3.2	. 2 |- ( ( ph /\ ps ) -> ch )
2		mpd3an3.3	. . 3 |- ( ( ph /\ ps /\ ch ) -> th )
3	2	3expa 1104	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
4	1, 3	mpdan 398	1 |- ( ( ph /\ ps ) -> th )

Syntax hints:   -> wi 4   /\ wa 97   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  stoic2b  1319  elovmpt2  5701  oav  6034  omv  6035  oeiv  6036  f1oeng  6237  mulpipq2  6469  ltrnqg  6518  genipv  6607  subval  7203  fzrevral3  8969  fzoval  9005  subsq2  9359