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Theorem 19.21bbi 1899
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 1809 . 2  |-  ( ph  ->  A. y ps )
3219.21bi 1809 1  |-  ( ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1368
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-12 1794
This theorem depends on definitions:  df-bi 185  df-ex 1588
This theorem is referenced by:  2mo  2369  2moOLD  2370  pocl  4759  funun  5571  fununi  5595  pm14.24  29854
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