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Theorem alanimi 1568
Description: Variant of al2imi 1567 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 1567 . 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 1546
This theorem is referenced by:  19.26  1600  alsyl  1622  vtoclgft  2947  euind  3066  reuind  3082  sbeqalb  3158  bm1.3ii  4276  trin2  5199  albitr  27229  2alanimi  27238
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563
This theorem depends on definitions:  df-bi 178  df-an 361
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