ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  equsb2 GIF version

Theorem equsb2 1744
Description: Substitution applied to an atomic wff. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
equsb2 [𝑦 / 𝑥]𝑦 = 𝑥

Proof of Theorem equsb2
StepHypRef Expression
1 sb2 1725 . 2 (∀𝑥(𝑥 = 𝑦𝑦 = 𝑥) → [𝑦 / 𝑥]𝑦 = 𝑥)
2 equcomi 1665 . 2 (𝑥 = 𝑦𝑦 = 𝑥)
31, 2mpg 1412 1 [𝑦 / 𝑥]𝑦 = 𝑥
Colors of variables: wff set class
Syntax hints:  wi 4  [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-8 1467  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-sb 1721
This theorem is referenced by:  sbco  1919
  Copyright terms: Public domain W3C validator