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Theorem nfopab 4276
 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 4270 . 2
2 nfv 1630 . . . . . 6
3 nfopab.1 . . . . . 6
42, 3nfan 1847 . . . . 5
54nfex 1866 . . . 4
65nfex 1866 . . 3
76nfab 2578 . 2
81, 7nfcxfr 2571 1
 Colors of variables: wff set class Syntax hints:   wa 360  wex 1551  wnf 1554   wceq 1653  cab 2424  wnfc 2561  cop 3819  copab 4268 This theorem is referenced by:  csbopabg  4286  nfmpt  4300  nfxp  4907  nfco  5041  nfcnv  5054 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-opab 4270
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