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Theorem alanimi 1418
Description: Variant of al2imi 1417 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 114 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
32al2imi 1417 . 2  |-  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) )
43imp 123 1  |-  ( ( A. x ph  /\  A. x ps )  ->  A. x ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103   A.wal 1312
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408
This theorem is referenced by:  19.26  1440  alsyl  1597  vtoclgft  2708  euind  2842  reuind  2860  sbeqalb  2935  bm1.3ii  4017  trin2  4898  bdbm1.3ii  12923
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