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Theorem sbcid 3419
Description: An identity theorem for substitution. See sbid 2100. (Contributed by Mario Carneiro, 18-Feb-2017.)
Assertion
Ref Expression
sbcid ([𝑥 / 𝑥]𝜑𝜑)

Proof of Theorem sbcid
StepHypRef Expression
1 sbsbc 3406 . 2 ([𝑥 / 𝑥]𝜑[𝑥 / 𝑥]𝜑)
2 sbid 2100 . 2 ([𝑥 / 𝑥]𝜑𝜑)
31, 2bitr3i 265 1 ([𝑥 / 𝑥]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 195  [wsb 1867  [wsbc 3402
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034  ax-ext 2590
This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-sbc 3403
This theorem is referenced by:  csbid  3507  snfil  21478  ex-natded9.26  26668  bnj605  30231  dedths  33266  frege93  37270
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