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Theorem 19.21bbi 1892
Description: Inference removing double quantifier. Version of 19.21bi 1891 with two quanditiers. (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 1891 . 2  |-  ( ph  ->  A. y ps )
3219.21bi 1891 1  |-  ( ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1401
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1637  ax-4 1650  ax-5 1723  ax-6 1769  ax-7 1812  ax-12 1876
This theorem depends on definitions:  df-bi 185  df-ex 1632
This theorem is referenced by:  2mo  2322  2moOLD  2323  pocl  4748  funun  5565  fununi  5589  trclfvcotr  12897  pm14.24  36151
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