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Theorem alanimi 1685
Description: Variant of al2imi 1684 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
StepHypRef Expression
1 alanimi.1 . . . 4  |-  ( (
ph  /\  ps )  ->  ch )
21ex 436 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
32al2imi 1684 . 2  |-  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) )
43imp 431 1  |-  ( ( A. x ph  /\  A. x ps )  ->  A. x ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 371   A.wal 1436
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679
This theorem depends on definitions:  df-bi 189  df-an 373
This theorem is referenced by:  19.26  1726  alsyl  1748  nfeqf  2101  bm1.1  2406  vtoclgft  3130  euind  3259  reuind  3276  sbeqalb  3353  bm1.3ii  4547  trin2  5240  bj-cbv3ta  31264  mpt2bi123f  32326  mptbi12f  32330  albitr  36576  2alanimi  36585
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