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Theorem sb4e 1664
Description: One direction of a simplified definition of substitution that unlike sb4 1691 doesn't require a distinctor antecedent. (Contributed by NM, 2-Feb-2007.)
Assertion
Ref Expression
sb4e ([y / x]φx(x = yyφ))

Proof of Theorem sb4e
StepHypRef Expression
1 sb1 1627 . 2 ([y / x]φx(x = y φ))
2 equs5e 1654 . 2 (x(x = y φ) → x(x = yyφ))
31, 2syl 14 1 ([y / x]φx(x = yyφ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wal 1224  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  ax-ia3 101  ax-5 1312  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-11 1374  ax-4 1377  ax-ial 1405
This theorem depends on definitions:  df-bi 110  df-sb 1624
This theorem is referenced by:  hbsb2e  1666
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