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Theorem 19.21t 1519
Description: Closed form of Theorem 19.21 of [Margaris] p. 90. (Contributed by NM, 27-May-1997.)
Assertion
Ref Expression
19.21t  |-  ( F/ x ph  ->  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) ) )

Proof of Theorem 19.21t
StepHypRef Expression
1 df-nf 1395 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 19.21ht 1518 . 2  |-  ( A. x ( ph  ->  A. x ph )  -> 
( A. x (
ph  ->  ps )  <->  ( ph  ->  A. x ps )
) )
31, 2sylbi 119 1  |-  ( F/ x ph  ->  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   A.wal 1287   F/wnf 1394
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-4 1445  ax-ial 1472  ax-i5r 1473
This theorem depends on definitions:  df-bi 115  df-nf 1395
This theorem is referenced by:  19.21  1520  nfimd  1522  equs5or  1758  sbal1yz  1925  r19.21t  2448  ceqsalt  2645  sbciegft  2869
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