Theorem anim12ii 343

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 276	. 2 |- ( ( ph /\ th ) -> ( ps -> ch ) )
3		anim12ii.2	. . 3 |- ( th -> ( ps -> ta ) )
4	3	adantl 277	. 2 |- ( ( ph /\ th ) -> ( ps -> ta ) )
5	2, 4	jcad 307	1 |- ( ( ph /\ th ) -> ( ps -> ( ch /\ ta ) ) )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  euim  2094  elex22  2752  tz7.2  4353  funcnvuni  5283  bj-findis  14582