Theorem alanimi 1473

Description: Variant of al2imi 1472 with conjunctive antecedent. (Contributed by Andrew Salmon, 8-Jun-2011.)

Hypothesis

Ref	Expression
alanimi.1	|- ( ( ph /\ ps ) -> ch )

Assertion

Ref	Expression
alanimi	|- ( ( A. x ph /\ A. x ps ) -> A. x ch )

Proof of Theorem alanimi

Step	Hyp	Ref	Expression
1		alanimi.1	. . . 4 |- ( ( ph /\ ps ) -> ch )
2	1	ex 115	. . 3 |- ( ph -> ( ps -> ch ) )
3	2	al2imi 1472	. 2 |- ( A. x ph -> ( A. x ps -> A. x ch ) )
4	3	imp 124	1 |- ( ( A. x ph /\ A. x ps ) -> A. x ch )

Syntax hints:   -> wi 4   /\ wa 104   A.wal 1362

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1461  ax-gen 1463

This theorem is referenced by:  19.26  1495  alsyl  1649  vtoclgft  2814  euind  2951  reuind  2969  sbeqalb  3046  bm1.3ii  4155  trin2  5062  bdbm1.3ii  15621