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Theorem sbf 1733
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 1482 . 2 (𝜑 → ∀𝑥𝜑)
32sbh 1732 1 ([𝑦 / 𝑥]𝜑𝜑)
Colors of variables: wff set class
Syntax hints:  wb 104  wnf 1419  [wsb 1718
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-i9 1493  ax-ial 1497
This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719
This theorem is referenced by:  sbf2  1734  sbequ5  1738  sbequ6  1739  sbt  1740  sblim  1906  moimv  2041  moanim  2049  sbabel  2282  nfcdeq  2877  oprcl  3697
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