Theorem mp3anr3 1231

Description: An inference based on modus ponens. (Contributed by NM, 19-Oct-2007.)

Hypotheses

Ref	Expression
mp3anr3.1	|- th
mp3anr3.2	|- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )

Assertion

Ref	Expression
mp3anr3	|- ( ( ph /\ ( ps /\ ch ) ) -> ta )

Proof of Theorem mp3anr3

Step	Hyp	Ref	Expression
1		mp3anr3.1	. . 3 |- th
2		mp3anr3.2	. . . 4 |- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )
3	2	ancoms 255	. . 3 |- ( ( ( ps /\ ch /\ th ) /\ ph ) -> ta )
4	1, 3	mp3anl3 1228	. 2 |- ( ( ( ps /\ ch ) /\ ph ) -> ta )
5	4	ancoms 255	1 |- ( ( ph /\ ( ps /\ ch ) ) -> ta )

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: (None)