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Theorem rabex 3892
Description: Separation Scheme in terms of a restricted class abstraction. (Contributed by NM, 19-Jul-1996.)
Hypothesis
Ref Expression
rabex.1 A V
Assertion
Ref Expression
rabex {x Aφ} V
Distinct variable group:   x,A
Allowed substitution hint:   φ(x)

Proof of Theorem rabex
StepHypRef Expression
1 rabex.1 . 2 A V
2 rabexg 3891 . 2 (A V → {x Aφ} V)
31, 2ax-mp 7 1 {x Aφ} V
Colors of variables: wff set class
Syntax hints:   wcel 1390  {crab 2304  Vcvv 2551
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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rab 2309  df-v 2553  df-in 2918  df-ss 2925
This theorem is referenced by:  repizf2  3906  ordtriexmidlem  4208  onsucelsucexmidlem  4214  regexmid  4219  nnregexmid  4285  ssimaex  5177  acexmidlemcase  5450  acexmidlemv  5453  ssfiexmid  6254  genpelvl  6494  genpelvu  6495  genipdm  6498  ltexprlemell  6571  ltexprlemelu  6572  cauappcvgprlemm  6616  cauappcvgprlemopl  6617  cauappcvgprlemlol  6618  cauappcvgprlemopu  6619  cauappcvgprlemupu  6620  cauappcvgprlemdisj  6622  cauappcvgprlemloc  6623  cauappcvgprlemladdfu  6625  cauappcvgprlemladdfl  6626  cauappcvgprlemladdru  6627  cauappcvgprlemladdrl  6628  cauappcvgprlem1  6630  cauappcvgprlem2  6631  dfuzi  8104  uzval  8231  ixxval  8515  fzval  8626
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