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Theorem sbcid 3612
Description: An identity theorem for substitution. See sbid 2279. (Contributed by Mario Carneiro, 18-Feb-2017.)
Assertion
Ref Expression
sbcid ([𝑥 / 𝑥]𝜑𝜑)

Proof of Theorem sbcid
StepHypRef Expression
1 sbsbc 3599 . 2 ([𝑥 / 𝑥]𝜑[𝑥 / 𝑥]𝜑)
2 sbid 2279 . 2 ([𝑥 / 𝑥]𝜑𝜑)
31, 2bitr3i 268 1 ([𝑥 / 𝑥]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 197  [wsb 2061  [wsbc 3595
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2069  ax-7 2105  ax-9 2164  ax-12 2211  ax-ext 2742
This theorem depends on definitions:  df-bi 198  df-an 385  df-ex 1875  df-sb 2062  df-clab 2751  df-cleq 2757  df-clel 2760  df-sbc 3596
This theorem is referenced by:  csbid  3698  snfil  21946  ex-natded9.26  27669  bnj605  31356  dedths  34850  frege93  38856
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