Theorem anim12dan 600

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  5133  isocnv  5893  f1oiso  5908  f1oiso2  5909  f1o2ndf1  6327  xpf1o  6956  pc11  12729  imasaddfnlemg  13221  imasaddflemg  13223  mhmpropd  13373  ghmsub  13662  invrpropdg  13986  znidom  14494  tgclb  14612  innei  14710  txcn  14822  plymullem1  15295  lgsdir2  15585