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Theorem sbf 1770
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 1512 . 2 (𝜑 → ∀𝑥𝜑)
32sbh 1769 1 ([𝑦 / 𝑥]𝜑𝜑)
Colors of variables: wff set class
Syntax hints:  wb 104  wnf 1453  [wsb 1755
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 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-i9 1523  ax-ial 1527
This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756
This theorem is referenced by:  sbf2  1771  sbequ5  1775  sbequ6  1776  sbt  1777  sblim  1950  moimv  2085  moanim  2093  sbabel  2339  nfcdeq  2952  oprcl  3789
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