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Theorem alanimi 1393
Description: Variant of al2imi 1392 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 113 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
32al2imi 1392 . 2  |-  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) )
43imp 122 1  |-  ( ( A. x ph  /\  A. x ps )  ->  A. x ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102   A.wal 1287
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383
This theorem is referenced by:  19.26  1415  alsyl  1571  vtoclgft  2669  euind  2800  reuind  2818  sbeqalb  2893  bm1.3ii  3952  trin2  4810  bdbm1.3ii  11439
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