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Theorem rdgeq2 7097
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 variable is distinct from all other variables.
StepHypRef Expression
1 ifeq1 3945 . . . 4
21mpteq2dv 4539 . . 3
3 recseq 7062 . . 3
42, 3syl 16 . 2
5 df-rdg 7095 . 2
6 df-rdg 7095 . 2
74, 5, 63eqtr4g 2523 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395   cvv 3109   c0 3784  ifcif 3941  U.cuni 4249  e.cmpt 4510  Limwlim 4884  domcdm 5004  rancrn 5005  `cfv 5593  recscrecs 7060  reccrdg 7094
This theorem is referenced by:  rdgeq12  7098  rdg0g  7112  oav  7180  itunifval  8817  hsmex  8833  ltweuz  12072  seqeq1  12110  dfrdg2  29228  trpredeq3  29305
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-un 3480  df-if 3942  df-uni 4250  df-br 4453  df-opab 4511  df-mpt 4512  df-iota 5556  df-fv 5601  df-recs 7061  df-rdg 7095
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