Theorem mpd3an3

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

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

Proof

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