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Theorem sbequ2 1649
Description: An equality theorem for substitution. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbequ2 (x = y → ([y / x]φφ))

Proof of Theorem sbequ2
StepHypRef Expression
1 df-sb 1643 . 2 ([y / x]φ ↔ ((x = yφ) x(x = y φ)))
2 simpl 102 . . 3 (((x = yφ) x(x = y φ)) → (x = yφ))
32com12 27 . 2 (x = y → (((x = yφ) x(x = y φ)) → φ))
41, 3syl5bi 141 1 (x = y → ([y / x]φφ))
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
This theorem depends on definitions:  df-bi 110  df-sb 1643
This theorem is referenced by:  stdpc7  1650  sbequ12  1651  sbequi  1717  mo23  1938  mopick  1975
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