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Theorem 2al2imi 27671
Description: Removes two universal qunatifiers from a statement. (Contributed by Andrew Salmon, 24-May-2011.)
Hypothesis
Ref Expression
2al2imi.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
2al2imi  |-  ( A. x A. y ph  ->  ( A. x A. y ps  ->  A. x A. y ch ) )

Proof of Theorem 2al2imi
StepHypRef Expression
1 2al2imi.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21al2imi 1551 . 2  |-  ( A. y ph  ->  ( A. y ps  ->  A. y ch ) )
32al2imi 1551 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   A.wal 1530
This theorem is referenced by:  2alim  27678
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8  ax-gen 1536  ax-5 1547
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