Theorem anim12dan 602

Description: Conjoin antecedents and consequents in a deduction. (Contributed by Mario Carneiro, 12-May-2014.)

Hypotheses

Ref	Expression
anim12dan.1	|- ( ( ph /\ ps ) -> ch )
anim12dan.2	|- ( ( ph /\ th ) -> ta )

Assertion

Ref	Expression
anim12dan	|- ( ( ph /\ ( ps /\ th ) ) -> ( ch /\ ta ) )

Proof of Theorem anim12dan

Step	Hyp	Ref	Expression
1		anim12dan.1	. . . 4 |- ( ( ph /\ ps ) -> ch )
2	1	ex 115	. . 3 |- ( ph -> ( ps -> ch ) )
3		anim12dan.2	. . . 4 |- ( ( ph /\ th ) -> ta )
4	3	ex 115	. . 3 |- ( ph -> ( th -> ta ) )
5	2, 4	anim12d 335	. 2 |- ( ph -> ( ( ps /\ th ) -> ( ch /\ ta ) ) )
6	5	imp 124	1 |- ( ( ph /\ ( ps /\ th ) ) -> ( ch /\ ta ) )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  xpexr2m  5176  isocnv  5947  f1oiso  5962  f1oiso2  5963  f1o2ndf1  6388  xpf1o  7025  pc11  12894  imasaddfnlemg  13387  imasaddflemg  13389  mhmpropd  13539  ghmsub  13828  invrpropdg  14153  znidom  14661  tgclb  14779  innei  14877  txcn  14989  plymullem1  15462  lgsdir2  15752