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Theorem 19.3 1836
Description: A wff may be quantified with a variable not free in it. Theorem 19.3 of [Margaris] p. 89. (Contributed by NM, 12-Mar-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 1808 . 2  |-  ( A. x ph  ->  ph )
2 19.3.1 . . 3  |-  F/ x ph
32nfri 1822 . 2  |-  ( ph  ->  A. x ph )
41, 3impbii 188 1  |-  ( A. x ph  <->  ph )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184   A.wal 1377   F/wnf 1599
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-12 1803
This theorem depends on definitions:  df-bi 185  df-ex 1597  df-nf 1600
This theorem is referenced by:  19.27  1870  19.28  1871  19.16  1904  19.17  1905  19.37  1915  2eu4OLD  2391  axrep4  4562  zfcndrep  8988  zfcndpow  8990  zfcndac  8993  bj-alexbiex  33335  bj-alalbial  33337  bj-axrep4  33458
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