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Theorem sbid 1922
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 1676 . . 3 x = x
2 sbequ12 1919 . . 3 (x = x → (φ ↔ [x / x]φ))
31, 2ax-mp 5 . 2 (φ ↔ [x / x]φ)
43bicomi 193 1 ([x / x]φφ)
Colors of variables: wff setvar class
Syntax hints:  wb 176  [wsb 1648
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-sb 1649
This theorem is referenced by:  abid  2341  sbceq1a  3056  sbcid  3062  csbid  3143
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