Theorem mp3anr2 1422

Description: An inference based on modus ponens. (Contributed by NM, 24-Nov-2006.)

Hypotheses

Ref	Expression
mp3anr2.1	|- ch
mp3anr2.2	|- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )

Assertion

Ref	Expression
mp3anr2	|- ( ( ph /\ ( ps /\ th ) ) -> ta )

Proof of Theorem mp3anr2

Step	Hyp	Ref	Expression
1		mp3anr2.1	. . 3 |- ch
2		mp3anr2.2	. . . 4 |- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )
3	2	ancoms 469	. . 3 |- ( ( ( ps /\ ch /\ th ) /\ ph ) -> ta )
4	1, 3	mp3anl2 1419	. 2 |- ( ( ( ps /\ th ) /\ ph ) -> ta )
5	4	ancoms 469	1 |- ( ( ph /\ ( ps /\ th ) ) -> ta )

Syntax hints:   -> wi 4   /\ wa 384   /\ w3a 1037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039

This theorem is referenced by:  mulgp1  17574  vcz  27430  nvmdi  27503