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Theorem sbf 1787
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 1529 . 2  |-  ( ph  ->  A. x ph )
32sbh 1786 1  |-  ( [ y  /  x ] ph 
<-> 
ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 105   F/wnf 1470   [wsb 1772
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1457  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-4 1520  ax-i9 1540  ax-ial 1544
This theorem depends on definitions:  df-bi 117  df-nf 1471  df-sb 1773
This theorem is referenced by:  sbf2  1788  sbequ5  1792  sbequ6  1793  sbt  1794  sblim  1967  moimv  2102  moanim  2110  sbabel  2356  nfcdeq  2971  oprcl  3814
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