Theorem alanimi 1342

Description: Variant of al2imi 1341 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 402	. . 3 |- (ph -> (ps -> ch))
3	2	al2imi 1341	. 2 |- (A.xph -> (A.xps -> A.xch))
4	3	imp 377	1 |- ((A.xph /\ A.xps) -> A.xch)

Syntax hints:   -> wi 3   /\ wa 240  A.wal 1296

This theorem is referenced by:  sbeqalb 2503  alsyl 16309  albitr 16310  2alanimi 16319

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-4 1319  ax-5o 1321

This theorem depends on definitions:  df-bi 164  df-an 242

Copyright terms: Public domain