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Theorem 19.3 1791
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 1763 . 2  |-  ( A. x ph  ->  ph )
2 19.3.1 . . 3  |-  F/ x ph
32nfri 1778 . 2  |-  ( ph  ->  A. x ph )
41, 3impbii 181 1  |-  ( A. x ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 177   A.wal 1549   F/wnf 1553
This theorem is referenced by:  19.27  1841  19.28  1842  19.16  1883  19.17  1884  19.37  1894  equsalOLD  2000  2eu4  2363  axrep4  4316  zfcndrep  8481  zfcndpow  8483  zfcndac  8486  equsalNEW7  29424
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-ex 1551  df-nf 1554
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