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Theorem alanimi 1364
Description: Variant of al2imi 1363 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 112 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
32al2imi 1363 . 2  |-  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) )
43imp 119 1  |-  ( ( A. x ph  /\  A. x ps )  ->  A. x ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101   A.wal 1257
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354
This theorem is referenced by:  19.26  1386  alsyl  1542  vtoclgft  2621  euind  2751  reuind  2767  sbeqalb  2842  bm1.3ii  3906  trin2  4744  bdbm1.3ii  10398
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