Theorem mp3an12i 1331

Description: mp3an 1327 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 1317	. 2 |- ( th -> ta )
6	1, 5	syl 14	1 |- ( ch -> ta )

Syntax hints:   -> wi 4   /\ w3a 968

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 970

This theorem is referenced by:  map1  6778  suplocsrlempr  7748  geo2lim  11457  fprodge0  11578  fprodge1  11580  oddp1d2  11827  bezoutlema  11932  bezoutlemb  11933  pythagtriplem1  12197  exmidunben  12359  ismet  12984  isxmet  12985  coseq0negpitopi  13397  cosq34lt1  13411  cos02pilt1  13412  logdivlti  13442