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Theorem nfrdg 7035
 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 7031 . 2 recs
2 nfcv 2562 . . . 4
3 nfv 1726 . . . . 5
4 nfrdg.2 . . . . 5
5 nfv 1726 . . . . . 6
6 nfcv 2562 . . . . . 6
7 nfrdg.1 . . . . . . 7
8 nfcv 2562 . . . . . . 7
97, 8nffv 5810 . . . . . 6
105, 6, 9nfif 3911 . . . . 5
113, 4, 10nfif 3911 . . . 4
122, 11nfmpt 4480 . . 3
1312nfrecs 6999 . 2 recs
141, 13nfcxfr 2560 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1403  wnfc 2548  cvv 3056  c0 3735  cif 3882  cuni 4188   cmpt 4450   wlim 4820   cdm 4940   crn 4941  cfv 5523  recscrecs 6996  crdg 7030 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1637  ax-4 1650  ax-5 1723  ax-6 1769  ax-7 1812  ax-10 1859  ax-11 1864  ax-12 1876  ax-13 2024  ax-ext 2378 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 974  df-tru 1406  df-ex 1632  df-nf 1636  df-sb 1762  df-clab 2386  df-cleq 2392  df-clel 2395  df-nfc 2550  df-ral 2756  df-rex 2757  df-rab 2760  df-v 3058  df-dif 3414  df-un 3416  df-in 3418  df-ss 3425  df-nul 3736  df-if 3883  df-sn 3970  df-pr 3972  df-op 3976  df-uni 4189  df-br 4393  df-opab 4451  df-mpt 4452  df-iota 5487  df-fv 5531  df-recs 6997  df-rdg 7031 This theorem is referenced by:  rdgsucmptf  7049  rdgsucmptnf  7050  frsucmpt  7058  frsucmptn  7059  nfseq  12069  trpredlem1  29978  trpredrec  29989
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