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Theorem alanimi 1552
Description: Variant of al2imi 1551 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 423 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
32al2imi 1551 . 2  |-  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) )
43imp 418 1  |-  ( ( A. x ph  /\  A. x ps )  ->  A. x ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   A.wal 1530
This theorem is referenced by:  19.26  1583  alsyl  1605  vtoclgft  2847  euind  2965  reuind  2981  sbeqalb  3056  bm1.3ii  4160  trin2  5082  albitr  27661  2alanimi  27670
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547
This theorem depends on definitions:  df-bi 177  df-an 360
  Copyright terms: Public domain W3C validator