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Theorem alanimi 1571
Description: Variant of al2imi 1570 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 424 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
32al2imi 1570 . 2  |-  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) )
43imp 419 1  |-  ( ( A. x ph  /\  A. x ps )  ->  A. x ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359   A.wal 1549
This theorem is referenced by:  19.26  1603  alsyl  1625  vtoclgft  2994  euind  3113  reuind  3129  sbeqalb  3205  bm1.3ii  4325  trin2  5249  albitr  27526  2alanimi  27535  ax7w10AUX7  29599
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566
This theorem depends on definitions:  df-bi 178  df-an 361
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