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Theorem sbf 1714
Description: Substitution for a variable not free in a wff does not affect it. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 4-Oct-2016.)
Hypothesis
Ref Expression
sbf.1  |-  F/ x ph
Assertion
Ref Expression
sbf  |-  ( [ y  /  x ] ph 
<-> 
ph )

Proof of Theorem sbf
StepHypRef Expression
1 sbf.1 . . 3  |-  F/ x ph
21nfri 1464 . 2  |-  ( ph  ->  A. x ph )
32sbh 1713 1  |-  ( [ y  /  x ] ph 
<-> 
ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 104   F/wnf 1401   [wsb 1699
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1388  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-4 1452  ax-i9 1475  ax-ial 1479
This theorem depends on definitions:  df-bi 116  df-nf 1402  df-sb 1700
This theorem is referenced by:  sbf2  1715  sbequ5  1719  sbequ6  1720  sbt  1721  sblim  1886  moimv  2021  moanim  2029  sbabel  2261  nfcdeq  2851  oprcl  3668
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