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Theorem sbcbidv 3476
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 1840 . 2 𝑥𝜑
2 sbcbidv.1 . 2 (𝜑 → (𝜓𝜒))
31, 2sbcbid 3475 1 (𝜑 → ([𝐴 / 𝑥]𝜓[𝐴 / 𝑥]𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  [wsbc 3421
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-sbc 3422
This theorem is referenced by:  sbcbii  3477  opelopabsb  4950  opelopabgf  4960  opelopabf  4965  sbcfng  6004  sbcfg  6005  fmptsnd  6395  wrd2ind  13423  islmod  18799  elmptrab  21553  f1od2  29365  isomnd  29510  isorng  29608  indexa  33195  sdclem2  33205  sdclem1  33206  fdc  33208  sbcalf  33584  sbcexf  33585  hdmap1ffval  36600  hdmap1fval  36601  hdmapffval  36633  hdmapfval  36634  hgmapffval  36692  hgmapfval  36693  rexrabdioph  36873  rexfrabdioph  36874  2rexfrabdioph  36875  3rexfrabdioph  36876  4rexfrabdioph  36877  6rexfrabdioph  36878  7rexfrabdioph  36879  2sbc6g  38133  2sbc5g  38134
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