Theorem mp3anr1 1421

Description: An inference based on modus ponens. (Contributed by NM, 4-Nov-2006.)

Hypotheses

Ref	Expression
mp3anr1.1	|- ps
mp3anr1.2	|- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )

Assertion

Ref	Expression
mp3anr1	|- ( ( ph /\ ( ch /\ th ) ) -> ta )

Proof of Theorem mp3anr1

Step	Hyp	Ref	Expression
1		mp3anr1.1	. . 3 |- ps
2		mp3anr1.2	. . . 4 |- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )
3	2	ancoms 469	. . 3 |- ( ( ( ps /\ ch /\ th ) /\ ph ) -> ta )
4	1, 3	mp3anl1 1418	. 2 |- ( ( ( ch /\ th ) /\ ph ) -> ta )
5	4	ancoms 469	1 |- ( ( ph /\ ( ch /\ 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:  vc2OLD  27423  vc0  27429  vcm  27431  nvaddsub4  27512  nvpi  27522  nvge0  27528  ipval3  27564  ipidsq  27565  lnoadd  27613  lnosub  27614  dipsubdir  27703