Theorem alanimi 1452

Description: Variant of al2imi 1451 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 114	. . 3 |- ( ph -> ( ps -> ch ) )
3	2	al2imi 1451	. 2 |- ( A. x ph -> ( A. x ps -> A. x ch ) )
4	3	imp 123	1 |- ( ( A. x ph /\ A. x ps ) -> A. x ch )

Syntax hints:   -> wi 4   /\ wa 103   A.wal 1346

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442

This theorem is referenced by:  19.26  1474  alsyl  1628  vtoclgft  2780  euind  2917  reuind  2935  sbeqalb  3011  bm1.3ii  4110  trin2  5002  bdbm1.3ii  13926