Theorem alanimi 1744

Description: Variant of al2imi 1743 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 450	. . 3 |- ( ph -> ( ps -> ch ) )
3	2	al2imi 1743	. 2 |- ( A. x ph -> ( A. x ps -> A. x ch ) )
4	3	imp 445	1 |- ( ( A. x ph /\ A. x ps ) -> A. x ch )

Syntax hints:   -> wi 4   /\ wa 384   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  19.26  1798  alsyl  1820  ax13  2249  nfeqf  2301  bm1.1  2607  vtoclgft  3254  vtoclgftOLD  3255  euind  3393  reuind  3411  sbeqalb  3488  bm1.3ii  4784  trin2  5519  bj-cbv3ta  32710  mpt2bi123f  33971  mptbi12f  33975  cotrintab  37921  albitr  38562  2alanimi  38571