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Theorem 2alanimi 27670
Description: Removes two universal quantifiers from a statement. (Contributed by Andrew Salmon, 24-May-2011.)
Hypothesis
Ref Expression
2alanimi.1  |-  ( (
ph  /\  ps )  ->  ch )
Assertion
Ref Expression
2alanimi  |-  ( ( A. x A. y ph  /\  A. x A. y ps )  ->  A. x A. y ch )

Proof of Theorem 2alanimi
StepHypRef Expression
1 2alanimi.1 . . 3  |-  ( (
ph  /\  ps )  ->  ch )
21alanimi 1552 . 2  |-  ( ( A. y ph  /\  A. y ps )  ->  A. y ch )
32alanimi 1552 1  |-  ( ( A. x A. y ph  /\  A. x A. y ps )  ->  A. x A. y ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   A.wal 1530
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