Theorem anim12dan 810

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 423	. . 3 |- (ph -> (ps -> ch))
3		anim12dan.2	. . . 4 |- ((ph /\ th) -> ta)
4	3	ex 423	. . 3 |- (ph -> (th -> ta))
5	2, 4	anim12d 546	. 2 |- (ph -> ((ps /\ th) -> (ch /\ ta)))
6	5	imp 418	1 |- ((ph /\ (ps /\ th)) -> (ch /\ ta))

Syntax hints:   -> wi 4   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  xpexr2  5111  isocnv  5492  f1oiso2  5501