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Theorem sb1 1627
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 1624 . 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 1358  [wsb 1623
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 1624
This theorem is referenced by:  sbh  1637  sbiedh  1648  sb4a  1660  sb4e  1664  sbcof2  1669  sb4  1691  sb4or  1692  spsbe  1701  sbidm  1709  sb5rf  1710  bj-sbimedh  7210
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