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Theorem nfoprab 5557
 Description: Bound-variable hypothesis builder for an operation class abstraction. (Contributed by NM, 22-Aug-2013.)
Hypothesis
Ref Expression
nfoprab.1
Assertion
Ref Expression
nfoprab
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,,,)

Proof of Theorem nfoprab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-oprab 5516 . 2
2 nfv 1421 . . . . . . 7
3 nfoprab.1 . . . . . . 7
42, 3nfan 1457 . . . . . 6
54nfex 1528 . . . . 5
65nfex 1528 . . . 4
76nfex 1528 . . 3
87nfab 2182 . 2
91, 8nfcxfr 2175 1
 Colors of variables: wff set class Syntax hints:   wa 97   wceq 1243  wnf 1349  wex 1381  cab 2026  wnfc 2165  cop 3378  coprab 5513 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-oprab 5516 This theorem is referenced by:  nfmpt2  5573
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