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Theorem alanimi 1656
Description: Variant of al2imi 1655 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 432 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
32al2imi 1655 . 2  |-  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) )
43imp 427 1  |-  ( ( A. x ph  /\  A. x ps )  ->  A. x ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367   A.wal 1401
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1637  ax-4 1650
This theorem depends on definitions:  df-bi 185  df-an 369
This theorem is referenced by:  19.26  1699  alsyl  1722  nfeqf  2069  bm1.1  2383  vtoclgft  3104  euind  3233  reuind  3250  sbeqalb  3327  bm1.3ii  4517  trin2  5330  bj-cbv3ta  30817  mpt2bi123f  31817  mptbi12f  31821  albitr  36080  2alanimi  36089
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