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Theorem sbf 1676
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 1428 . 2  |-  ( ph  ->  A. x ph )
32sbh 1675 1  |-  ( [ y  /  x ] ph 
<-> 
ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 102   F/wnf 1365   [wsb 1661
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-i9 1439  ax-ial 1443
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662
This theorem is referenced by:  sbf2  1677  sbequ5  1681  sbequ6  1682  sbt  1683  sblim  1847  moimv  1982  moanim  1990  sbabel  2219  nfcdeq  2784  oprcl  3601
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