ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sbf GIF version

Theorem sbf 1757
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 1499 . 2 (𝜑 → ∀𝑥𝜑)
32sbh 1756 1 ([𝑦 / 𝑥]𝜑𝜑)
Colors of variables: wff set class
Syntax hints:  wb 104  wnf 1440  [wsb 1742
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 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-4 1490  ax-i9 1510  ax-ial 1514
This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743
This theorem is referenced by:  sbf2  1758  sbequ5  1762  sbequ6  1763  sbt  1764  sblim  1937  moimv  2072  moanim  2080  sbabel  2326  nfcdeq  2934  oprcl  3767
  Copyright terms: Public domain W3C validator