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Theorem 19.3 1491
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 1446 . 2  |-  ( A. x ph  ->  ph )
2 19.3.1 . . 3  |-  F/ x ph
32nfri 1457 . 2  |-  ( ph  ->  A. x ph )
41, 3impbii 124 1  |-  ( A. x ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> 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-4 1445
This theorem depends on definitions:  df-bi 115  df-nf 1395
This theorem is referenced by:  19.16  1492  19.17  1493  19.27  1498  19.28  1500  19.37-1  1609  rexxfrd  4276
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