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Theorem sbcid 2895
Description: An identity theorem for substitution. See sbid 1730. (Contributed by Mario Carneiro, 18-Feb-2017.)
Assertion
Ref Expression
sbcid ([𝑥 / 𝑥]𝜑𝜑)

Proof of Theorem sbcid
StepHypRef Expression
1 sbsbc 2884 . 2 ([𝑥 / 𝑥]𝜑[𝑥 / 𝑥]𝜑)
2 sbid 1730 . 2 ([𝑥 / 𝑥]𝜑𝜑)
31, 2bitr3i 185 1 ([𝑥 / 𝑥]𝜑𝜑)
Colors of variables: wff set class
Syntax hints:  wb 104  [wsb 1718  [wsbc 2880
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-sbc 2881
This theorem is referenced by:  csbid  2980
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