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Theorem sbf 1657
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 xφ
Assertion
Ref Expression
sbf ([y / x]φφ)

Proof of Theorem sbf
StepHypRef Expression
1 sbf.1 . . 3 xφ
21nfri 1409 . 2 (φxφ)
32sbh 1656 1 ([y / x]φφ)
Colors of variables: wff set class
Syntax hints:  wb 98  wnf 1346  [wsb 1642
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-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643
This theorem is referenced by:  sbf2  1658  sbequ5  1662  sbequ6  1663  sbt  1664  sblim  1828  moimv  1963  moanim  1971  sbabel  2200  nfcdeq  2755  oprcl  3564
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