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Theorem sbcid 3794
Description: An identity theorem for substitution. See sbid 2246. (Contributed by Mario Carneiro, 18-Feb-2017.)
Assertion
Ref Expression
sbcid ([𝑥 / 𝑥]𝜑𝜑)

Proof of Theorem sbcid
StepHypRef Expression
1 sbsbc 3781 . 2 ([𝑥 / 𝑥]𝜑[𝑥 / 𝑥]𝜑)
2 sbid 2246 . 2 ([𝑥 / 𝑥]𝜑𝜑)
31, 2bitr3i 277 1 ([𝑥 / 𝑥]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 205  [wsb 2066  [wsbc 3777
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-12 2170  ax-ext 2702
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723  df-clel 2809  df-sbc 3778
This theorem is referenced by:  csbid  3906  snfil  23688  ex-natded9.26  30105  bnj605  34382  dedths  38296  frege93  43170  or2expropbilem1  46201
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