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Theorem nfopab 4627
 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 4623 . 2
2 nfv 1619 . . . . . 6
3 nfopab.1 . . . . . 6
42, 3nfan 1824 . . . . 5
54nfex 1843 . . . 4
65nfex 1843 . . 3
76nfab 2493 . 2
81, 7nfcxfr 2486 1
 Colors of variables: wff setvar class Syntax hints:   wa 358  wex 1541  wnf 1544   wceq 1642  cab 2339  wnfc 2476  cop 4561  copab 4622 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-opab 4623 This theorem is referenced by:  csbopabg  4637  nfxp  4810  nfco  4882  nfcnv  4891  nfmpt  5671
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