Theorem anim12dan 608

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 ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  xpexr2m  5229  isocnv  6017  f1oiso  6032  f1oiso2  6033  f1o2ndf1  6464  xpf1o  7144  pc11  13130  imasaddfnlemg  13684  imasaddflemg  13686  mhmpropd  13822  ghmsub  14103  invrpropdg  14505  znidom  15041  tgclb  15215  innei  15313  txcn  15425  plymullem1  15898  lgsdir2  16250