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Theorem nfrdg 6664
 Description: Bound-variable hypothesis builder for the recursive definition generator. (Contributed by NM, 14-Sep-2003.) (Revised by Mario Carneiro, 8-Sep-2013.)
Hypotheses
Ref Expression
nfrdg.1
nfrdg.2
Assertion
Ref Expression
nfrdg

Proof of Theorem nfrdg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-rdg 6660 . 2 recs
2 nfcv 2571 . . . 4
3 nfv 1629 . . . . 5
4 nfrdg.2 . . . . 5
5 nfv 1629 . . . . . 6
6 nfcv 2571 . . . . . 6
7 nfrdg.1 . . . . . . 7
8 nfcv 2571 . . . . . . 7
97, 8nffv 5727 . . . . . 6
105, 6, 9nfif 3755 . . . . 5
113, 4, 10nfif 3755 . . . 4
122, 11nfmpt 4289 . . 3
1312nfrecs 6627 . 2 recs
141, 13nfcxfr 2568 1
 Colors of variables: wff set class Syntax hints:   wceq 1652  wnfc 2558  cvv 2948  c0 3620  cif 3731  cuni 4007   cmpt 4258   wlim 4574   cdm 4870   crn 4871  cfv 5446  recscrecs 6624  crdg 6659 This theorem is referenced by:  rdgsucmptf  6678  rdgsucmptnf  6679  frsucmpt  6687  frsucmptn  6688  nfseq  11325  trpredlem1  25497  trpredrec  25508 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-mpt 4260  df-iota 5410  df-fv 5454  df-recs 6625  df-rdg 6660
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