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Theorem sbcid 3761
Description: An identity theorem for substitution. See sbid 2248. (Contributed by Mario Carneiro, 18-Feb-2017.)
Assertion
Ref Expression
sbcid ([𝑥 / 𝑥]𝜑𝜑)

Proof of Theorem sbcid
StepHypRef Expression
1 sbsbc 3748 . 2 ([𝑥 / 𝑥]𝜑[𝑥 / 𝑥]𝜑)
2 sbid 2248 . 2 ([𝑥 / 𝑥]𝜑𝜑)
31, 2bitr3i 277 1 ([𝑥 / 𝑥]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 205  [wsb 2068  [wsbc 3744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-12 2172  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-sbc 3745
This theorem is referenced by:  csbid  3873  snfil  23231  ex-natded9.26  29405  bnj605  33559  dedths  37453  frege93  42302  or2expropbilem1  45340
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