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Theorem nfoprab 6362
 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 6312 . 2
2 nfv 1769 . . . . . . 7
3 nfoprab.1 . . . . . . 7
42, 3nfan 2031 . . . . . 6
54nfex 2050 . . . . 5
65nfex 2050 . . . 4
76nfex 2050 . . 3
87nfab 2616 . 2
91, 8nfcxfr 2610 1
 Colors of variables: wff setvar class Syntax hints:   wa 376   wceq 1452  wex 1671  wnf 1675  cab 2457  wnfc 2599  cop 3965  coprab 6309 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-oprab 6312 This theorem is referenced by:  nfmpt2  6379
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