Theorem anim12dan 589

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 114	. . 3 |- ( ph -> ( ps -> ch ) )
3		anim12dan.2	. . . 4 |- ( ( ph /\ th ) -> ta )
4	3	ex 114	. . 3 |- ( ph -> ( th -> ta ) )
5	2, 4	anim12d 333	. 2 |- ( ph -> ( ( ps /\ th ) -> ( ch /\ ta ) ) )
6	5	imp 123	1 |- ( ( ph /\ ( ps /\ th ) ) -> ( ch /\ ta ) )

Syntax hints:   -> wi 4   /\ wa 103

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

This theorem is referenced by:  xpexr2m  4975  isocnv  5705  f1oiso  5720  f1oiso2  5721  f1o2ndf1  6118  xpf1o  6731  tgclb  12223  innei  12321  txcn  12433