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Theorem nfopab 3816
 Description: Bound-variable hypothesis builder for class abstraction. (Contributed by NM, 1-Sep-1999.) (Unnecessary distinct variable restrictions were removed by Andrew Salmon, 11-Jul-2011.)
Hypothesis
Ref Expression
nfopab.1
Assertion
Ref Expression
nfopab
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem nfopab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-opab 3810 . 2
2 nfv 1418 . . . . . 6
3 nfopab.1 . . . . . 6
42, 3nfan 1454 . . . . 5
54nfex 1525 . . . 4
65nfex 1525 . . 3
76nfab 2179 . 2
81, 7nfcxfr 2172 1
 Colors of variables: wff set class Syntax hints:   wa 97   wceq 1242  wnf 1346  wex 1378  cab 2023  wnfc 2162  cop 3370  copab 3808 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-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-opab 3810 This theorem is referenced by:  csbopabg  3826  nfmpt  3840  nfxp  4314  nfco  4444  nfcnv  4457
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