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Theorem sbcid 2839
Description: An identity theorem for substitution. See sbid 1699. (Contributed by Mario Carneiro, 18-Feb-2017.)
Assertion
Ref Expression
sbcid ([𝑥 / 𝑥]𝜑𝜑)

Proof of Theorem sbcid
StepHypRef Expression
1 sbsbc 2828 . 2 ([𝑥 / 𝑥]𝜑[𝑥 / 𝑥]𝜑)
2 sbid 1699 . 2 ([𝑥 / 𝑥]𝜑𝜑)
31, 2bitr3i 184 1 ([𝑥 / 𝑥]𝜑𝜑)
Colors of variables: wff set class
Syntax hints:  wb 103  [wsb 1687  [wsbc 2824
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-sbc 2825
This theorem is referenced by:  csbid  2924
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