Theorem mp3an12i 1330

Description: mp3an 1326 with antecedents in standard conjunction form and with one hypothesis an implication. (Contributed by Alan Sare, 28-Aug-2016.)

Hypotheses

Ref	Expression
mp3an12i.1	|- ph
mp3an12i.2	|- ps
mp3an12i.3	|- ( ch -> th )
mp3an12i.4	|- ( ( ph /\ ps /\ th ) -> ta )

Assertion

Ref	Expression
mp3an12i	|- ( ch -> ta )

Proof of Theorem mp3an12i

Step	Hyp	Ref	Expression
1		mp3an12i.3	. 2 |- ( ch -> th )
2		mp3an12i.1	. . 3 |- ph
3		mp3an12i.2	. . 3 |- ps
4		mp3an12i.4	. . 3 |- ( ( ph /\ ps /\ th ) -> ta )
5	2, 3, 4	mp3an12 1316	. 2 |- ( th -> ta )
6	1, 5	syl 14	1 |- ( ch -> ta )

Syntax hints:   -> wi 4   /\ w3a 967

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 969

This theorem is referenced by:  map1  6769  suplocsrlempr  7739  geo2lim  11443  fprodge0  11564  fprodge1  11566  oddp1d2  11812  bezoutlema  11917  bezoutlemb  11918  pythagtriplem1  12174  exmidunben  12296  ismet  12885  isxmet  12886  coseq0negpitopi  13298  cosq34lt1  13312  cos02pilt1  13313  logdivlti  13343