ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sb1 Structured version   GIF version

Theorem sb1 1646
Description: One direction of a simplified definition of substitution. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sb1 ([y / x]φx(x = y φ))

Proof of Theorem sb1
StepHypRef Expression
1 df-sb 1643 . 2 ([y / x]φ ↔ ((x = yφ) x(x = y φ)))
21simprbi 260 1 ([y / x]φx(x = y φ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wex 1378  [wsb 1642
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100
This theorem depends on definitions:  df-bi 110  df-sb 1643
This theorem is referenced by:  sbh  1656  sbiedh  1667  sb4a  1679  sb4e  1683  sbcof2  1688  sb4  1710  sb4or  1711  spsbe  1720  sbidm  1728  sb5rf  1729  bj-sbimedh  9226
  Copyright terms: Public domain W3C validator