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Theorem sb1 1651
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 1649 . 2 ([y / x]φ ↔ ((x = yφ) x(x = y φ)))
21simprbi 450 1 ([y / x]φx(x = y φ))
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358  wex 1541  [wsb 1648
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-sb 1649
This theorem is referenced by:  sb4a  1923  sb4e  1924  sbft  2025  sbied  2036  sb4  2053  sbn  2062  sb5rf  2090
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