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Theorem 19.21bbi 1888
Description: Inference removing double quantifier. (Contributed by NM, 20-Apr-1994.)
Hypothesis
Ref Expression
19.21bbi.1  |-  ( ph  ->  A. x A. y ps )
Assertion
Ref Expression
19.21bbi  |-  ( ph  ->  ps )

Proof of Theorem 19.21bbi
StepHypRef Expression
1 19.21bbi.1 . . 3  |-  ( ph  ->  A. x A. y ps )
2119.21bi 1774 . 2  |-  ( ph  ->  A. y ps )
3219.21bi 1774 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1549
This theorem is referenced by:  pocl  4502  funun  5487  fununi  5509  pm14.24  27600
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-ex 1551
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