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Theorem sbid 1654
Description: An identity theorem for substitution. Remark 9.1 in [Megill] p. 447 (p. 15 of the preprint). (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbid ([x / x]φφ)

Proof of Theorem sbid
StepHypRef Expression
1 equid 1586 . . 3 x = x
2 sbequ12 1651 . . 3 (x = x → (φ ↔ [x / x]φ))
31, 2ax-mp 7 . 2 (φ ↔ [x / x]φ)
43bicomi 123 1 ([x / x]φφ)
Colors of variables: wff set class
Syntax hints:  wb 98  [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-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420
This theorem depends on definitions:  df-bi 110  df-sb 1643
This theorem is referenced by:  abid  2025  sbceq1a  2767  sbcid  2773
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