ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  19.3 Unicode version

Theorem 19.3 1446
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 1401 . 2  |-  ( A. x ph  ->  ph )
2 19.3.1 . . 3  |-  F/ x ph
32nfri 1412 . 2  |-  ( ph  ->  A. x ph )
41, 3impbii 117 1  |-  ( A. x ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 98   A.wal 1241   F/wnf 1349
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-4 1400
This theorem depends on definitions:  df-bi 110  df-nf 1350
This theorem is referenced by:  19.16  1447  19.17  1448  19.27  1453  19.28  1455  19.37-1  1564  rexxfrd  4195
  Copyright terms: Public domain W3C validator