Theorem anim12dan 604

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  5178  isocnv  5952  f1oiso  5967  f1oiso2  5968  f1o2ndf1  6393  xpf1o  7030  pc11  12922  imasaddfnlemg  13415  imasaddflemg  13417  mhmpropd  13567  ghmsub  13856  invrpropdg  14182  znidom  14690  tgclb  14808  innei  14906  txcn  15018  plymullem1  15491  lgsdir2  15781