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Theorem sbf 1735
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 1484 . 2 (𝜑 → ∀𝑥𝜑)
32sbh 1734 1 ([𝑦 / 𝑥]𝜑𝜑)
Colors of variables: wff set class
Syntax hints:  wb 104  wnf 1421  [wsb 1720
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 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-i9 1495  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721
This theorem is referenced by:  sbf2  1736  sbequ5  1740  sbequ6  1741  sbt  1742  sblim  1908  moimv  2043  moanim  2051  sbabel  2284  nfcdeq  2879  oprcl  3699
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