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Theorem 19.21bbi 1877
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 1766 . 2  |-  ( ph  ->  A. y ps )
3219.21bi 1766 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1546
This theorem is referenced by:  pocl  4453  funun  5437  fununi  5459  pm14.24  27303
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-11 1753
This theorem depends on definitions:  df-bi 178  df-ex 1548
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