Theorem alanimi 1388

Description: Variant of al2imi 1387 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 113	. . 3 |- ( ph -> ( ps -> ch ) )
3	2	al2imi 1387	. 2 |- ( A. x ph -> ( A. x ps -> A. x ch ) )
4	3	imp 122	1 |- ( ( A. x ph /\ A. x ps ) -> A. x ch )

Syntax hints:   -> wi 4   /\ wa 102   A.wal 1282

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378

This theorem is referenced by:  19.26  1410  alsyl  1566  vtoclgft  2649  euind  2779  reuind  2795  sbeqalb  2870  bm1.3ii  3899  trin2  4736  bdbm1.3ii  10682