ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sbf2 GIF version

Theorem sbf2 1736
Description: Substitution has no effect on a bound variable. (Contributed by NM, 1-Jul-2005.)
Assertion
Ref Expression
sbf2 ([𝑦 / 𝑥]∀𝑥𝜑 ↔ ∀𝑥𝜑)

Proof of Theorem sbf2
StepHypRef Expression
1 nfa1 1506 . 2 𝑥𝑥𝜑
21sbf 1735 1 ([𝑦 / 𝑥]∀𝑥𝜑 ↔ ∀𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  wb 104  wal 1314  [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: (None)
  Copyright terms: Public domain W3C validator