Theorem alanimi 1562

Description: Variant of al2imi 1561 with conjunctive antecedent. (Contributed by Andrew Salmon, 8-Jun-2011.)

Hypothesis

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

Assertion

Ref	Expression
alanimi	|- ((A.xph /\ A.xps) -> A.xch)

Proof of Theorem alanimi

Step	Hyp	Ref	Expression
1		alanimi.1	. . . 4 |- ((ph /\ ps) -> ch)
2	1	ex 423	. . 3 |- (ph -> (ps -> ch))
3	2	al2imi 1561	. 2 |- (A.xph -> (A.xps -> A.xch))
4	3	imp 418	1 |- ((A.xph /\ A.xps) -> A.xch)

Syntax hints:   -> wi 4   /\ wa 358  A.wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  19.26  1593  alsyl  1615  vtoclgft  2906  euind  3024  reuind  3040  sbeqalb  3099