Theorem alanimi 1348

Description: Variant of al2imi 1347 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 108	. . 3 |- ( ph -> ( ps -> ch ) )
3	2	al2imi 1347	. 2 |- ( A. x ph -> ( A. x ps -> A. x ch ) )
4	3	imp 115	1 |- ( ( A. x ph /\ A. x ps ) -> A. x ch )

Syntax hints:   -> wi 4   /\ wa 97   A.wal 1241

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338

This theorem is referenced by:  19.26  1370  alsyl  1526  vtoclgft  2604  euind  2728  reuind  2744  sbeqalb  2815  bm1.3ii  3878  trin2  4716  bdbm1.3ii  10011