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Theorem sbcid 3793
Description: An identity theorem for substitution. See sbid 2243. (Contributed by Mario Carneiro, 18-Feb-2017.)
Assertion
Ref Expression
sbcid ([𝑥 / 𝑥]𝜑𝜑)

Proof of Theorem sbcid
StepHypRef Expression
1 sbsbc 3780 . 2 ([𝑥 / 𝑥]𝜑[𝑥 / 𝑥]𝜑)
2 sbid 2243 . 2 ([𝑥 / 𝑥]𝜑𝜑)
31, 2bitr3i 277 1 ([𝑥 / 𝑥]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 205  [wsb 2060  [wsbc 3776
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-12 2167  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-sbc 3777
This theorem is referenced by:  csbid  3905  snfil  23767  ex-natded9.26  30228  bnj605  34538  dedths  38434  frege93  43386  or2expropbilem1  46414
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