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Theorem sbequ1 1648
Description: An equality theorem for substitution. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbequ1 (x = y → (φ → [y / x]φ))

Proof of Theorem sbequ1
StepHypRef Expression
1 pm3.4 316 . . 3 ((x = y φ) → (x = yφ))
2 19.8a 1479 . . 3 ((x = y φ) → x(x = y φ))
3 df-sb 1643 . . 3 ([y / x]φ ↔ ((x = yφ) x(x = y φ)))
41, 2, 3sylanbrc 394 . 2 ((x = y φ) → [y / x]φ)
54ex 108 1 (x = y → (φ → [y / x]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  ax-ia3 101  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397
This theorem depends on definitions:  df-bi 110  df-sb 1643
This theorem is referenced by:  sbequ12  1651  sbequi  1717  sb6rf  1730  mo2n  1925  bj-bdfindes  9383  bj-findes  9411
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