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Theorem rdgeq1 6268
 Description: Equality theorem for the recursive definition generator. (Contributed by NM, 9-Apr-1995.) (Revised by Mario Carneiro, 9-May-2015.)
Assertion
Ref Expression
rdgeq1

Proof of Theorem rdgeq1
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 fveq1 5420 . . . . . 6
21iuneq2d 3838 . . . . 5
32uneq2d 3230 . . . 4
43mpteq2dv 4019 . . 3
5 recseq 6203 . . 3 recs recs
64, 5syl 14 . 2 recs recs
7 df-irdg 6267 . 2 recs
8 df-irdg 6267 . 2 recs
96, 7, 83eqtr4g 2197 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1331  cvv 2686   cun 3069  ciun 3813   cmpt 3989   cdm 4539  cfv 5123  recscrecs 6201  crdg 6266 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-uni 3737  df-iun 3815  df-br 3930  df-opab 3990  df-mpt 3991  df-iota 5088  df-fv 5131  df-recs 6202  df-irdg 6267 This theorem is referenced by:  omv  6351  oeiv  6352
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