Theorem anim12dan 564

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 113	. . 3 |- ( ph -> ( ps -> ch ) )
3		anim12dan.2	. . . 4 |- ( ( ph /\ th ) -> ta )
4	3	ex 113	. . 3 |- ( ph -> ( th -> ta ) )
5	2, 4	anim12d 328	. 2 |- ( ph -> ( ( ps /\ th ) -> ( ch /\ ta ) ) )
6	5	imp 122	1 |- ( ( ph /\ ( ps /\ th ) ) -> ( ch /\ ta ) )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  xpexr2m  4782  isocnv  5471  f1oiso  5485  f1oiso2  5486  f1o2ndf1  5869