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Theorem rdgeq2 6199
 Description: Equality theorem for the recursive definition generator. (Contributed by NM, 9-Apr-1995.) (Revised by Mario Carneiro, 9-May-2015.)
Assertion
Ref Expression
rdgeq2

Proof of Theorem rdgeq2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 uneq1 3170 . . . 4
21mpteq2dv 3959 . . 3
3 recseq 6133 . . 3 recs recs
42, 3syl 14 . 2 recs recs
5 df-irdg 6197 . 2 recs
6 df-irdg 6197 . 2 recs
74, 5, 63eqtr4g 2157 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1299  cvv 2641   cun 3019  ciun 3760   cmpt 3929   cdm 4477  cfv 5059  recscrecs 6131  crdg 6196 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082 This theorem depends on definitions:  df-bi 116  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-ral 2380  df-rex 2381  df-v 2643  df-un 3025  df-uni 3684  df-br 3876  df-opab 3930  df-mpt 3931  df-iota 5024  df-fv 5067  df-recs 6132  df-irdg 6197 This theorem is referenced by:  rdg0g  6215  oav  6280
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