Theorem anim12ii 553

Description: Conjoin antecedents and consequents in a deduction. (Contributed by NM, 11-Nov-2007.) (Proof shortened by Wolf Lammen, 19-Jul-2013.)

Hypotheses

Ref	Expression
anim12ii.1	|- (ph -> (ps -> ch))
anim12ii.2	|- (th -> (ps -> ta))

Assertion

Ref	Expression
anim12ii	|- ((ph /\ th) -> (ps -> (ch /\ ta)))

Proof of Theorem anim12ii

Step	Hyp	Ref	Expression
1		anim12ii.1	. . 3 |- (ph -> (ps -> ch))
2	1	adantr 451	. 2 |- ((ph /\ th) -> (ps -> ch))
3		anim12ii.2	. . 3 |- (th -> (ps -> ta))
4	3	adantl 452	. 2 |- ((ph /\ th) -> (ps -> ta))
5	2, 4	jcad 519	1 |- ((ph /\ th) -> (ps -> (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:  euim  2254  elex22  2871  sfinltfin  4536  funcnvuni  5162