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Theorem sbcbidv 2817
 Description: Formula-building deduction rule 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 1421 . 2 𝑥𝜑
2 sbcbidv.1 . 2 (𝜑 → (𝜓𝜒))
31, 2sbcbid 2816 1 (𝜑 → ([𝐴 / 𝑥]𝜓[𝐴 / 𝑥]𝜒))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98  [wsbc 2764 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-sbc 2765 This theorem is referenced by:  sbcbii  2818  csbcomg  2873  opelopabsb  3997  opelopabf  4011  sbcfng  5044  sbcfg  5045
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