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Theorem 19.21t 1544
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 1420 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 19.21ht 1543 . 2  |-  ( A. x ( ph  ->  A. x ph )  -> 
( A. x (
ph  ->  ps )  <->  ( ph  ->  A. x ps )
) )
31, 2sylbi 120 1  |-  ( F/ x ph  ->  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1312   F/wnf 1419
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-4 1470  ax-ial 1497  ax-i5r 1498
This theorem depends on definitions:  df-bi 116  df-nf 1420
This theorem is referenced by:  19.21  1545  nfimd  1547  equs5or  1784  sbal1yz  1952  r19.21t  2482  ceqsalt  2684  sbciegft  2909
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