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Theorem sbcbidv 2897
Description: Formula-building deduction for class substitution. (Contributed by NM, 29-Dec-2014.)
Hypothesis
Ref Expression
sbcbidv.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
sbcbidv (𝜑 → ([𝐴 / 𝑥]𝜓[𝐴 / 𝑥]𝜒))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝜒(𝑥)   𝐴(𝑥)

Proof of Theorem sbcbidv
StepHypRef Expression
1 nfv 1466 . 2 𝑥𝜑
2 sbcbidv.1 . 2 (𝜑 → (𝜓𝜒))
31, 2sbcbid 2896 1 (𝜑 → ([𝐴 / 𝑥]𝜓[𝐴 / 𝑥]𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103  [wsbc 2840
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 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-sbc 2841
This theorem is referenced by:  sbcbii  2898  csbcomg  2954  opelopabsb  4087  opelopabf  4101  sbcfng  5159  sbcfg  5160  f1od2  6000
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