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Theorem sbcbidv 3005
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 1515 . 2 𝑥𝜑
2 sbcbidv.1 . 2 (𝜑 → (𝜓𝜒))
31, 2sbcbid 3004 1 (𝜑 → ([𝐴 / 𝑥]𝜓[𝐴 / 𝑥]𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104  [wsbc 2947
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 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-11 1493  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146
This theorem depends on definitions:  df-bi 116  df-tru 1345  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-sbc 2948
This theorem is referenced by:  sbcbii  3006  csbcomg  3064  opelopabsb  4233  opelopabf  4247  sbcfng  5330  sbcfg  5331  f1od2  6195
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