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Theorem sbsbc 2886
Description: Show that df-sb 1721 and df-sbc 2883 are equivalent when the class term 𝐴 in df-sbc 2883 is a setvar variable. This theorem lets us reuse theorems based on df-sb 1721 for proofs involving df-sbc 2883. (Contributed by NM, 31-Dec-2016.) (Proof modification is discouraged.)
Assertion
Ref Expression
sbsbc ([𝑦 / 𝑥]𝜑[𝑦 / 𝑥]𝜑)

Proof of Theorem sbsbc
StepHypRef Expression
1 eqid 2117 . 2 𝑦 = 𝑦
2 dfsbcq2 2885 . 2 (𝑦 = 𝑦 → ([𝑦 / 𝑥]𝜑[𝑦 / 𝑥]𝜑))
31, 2ax-mp 5 1 ([𝑦 / 𝑥]𝜑[𝑦 / 𝑥]𝜑)
Colors of variables: wff set class
Syntax hints:  wb 104  [wsb 1720  [wsbc 2882
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 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-17 1491  ax-ial 1499  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-clab 2104  df-cleq 2110  df-clel 2113  df-sbc 2883
This theorem is referenced by:  spsbc  2893  sbcid  2897  sbcco  2903  sbcco2  2904  sbcie2g  2914  eqsbc3  2920  sbcralt  2957  sbcrext  2958  sbnfc2  3030  csbabg  3031  cbvralcsf  3032  cbvrexcsf  3033  cbvreucsf  3034  cbvrabcsf  3035  isarep1  5179  finexdc  6764  ssfirab  6790  zsupcllemstep  11565  bezoutlemmain  11613  bdsbc  12983
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