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Theorem 19.3 1516
Description: A wff may be quantified with a variable not free in it. Theorem 19.3 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)
Hypothesis
Ref Expression
19.3.1  |-  F/ x ph
Assertion
Ref Expression
19.3  |-  ( A. x ph  <->  ph )

Proof of Theorem 19.3
StepHypRef Expression
1 sp 1471 . 2  |-  ( A. x ph  ->  ph )
2 19.3.1 . . 3  |-  F/ x ph
32nfri 1482 . 2  |-  ( ph  ->  A. x ph )
41, 3impbii 125 1  |-  ( A. x ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> 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-4 1470
This theorem depends on definitions:  df-bi 116  df-nf 1420
This theorem is referenced by:  19.16  1517  19.17  1518  19.27  1523  19.28  1525  19.37-1  1635  rexxfrd  4352
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