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Theorem nfopab 3964
 Description: Bound-variable hypothesis builder for class abstraction. (Contributed by NM, 1-Sep-1999.) Remove disjoint variable conditions. (Revised 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 3958 . 2
2 nfv 1491 . . . . . 6
3 nfopab.1 . . . . . 6
42, 3nfan 1527 . . . . 5
54nfex 1599 . . . 4
65nfex 1599 . . 3
76nfab 2261 . 2
81, 7nfcxfr 2253 1
 Colors of variables: wff set class Syntax hints:   wa 103   wceq 1314  wnf 1419  wex 1451  cab 2101  wnfc 2243  cop 3498  copab 3956 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-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-opab 3958 This theorem is referenced by:  csbopabg  3974  nfmpt  3988  nfxp  4534  nfco  4672  nfcnv  4686  nfofr  5954
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