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Theorem rdgeq1 7096
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 variable is distinct from all other variables.
StepHypRef Expression
1 fveq1 5870 . . . . . 6
21ifeq2d 3960 . . . . 5
32ifeq2d 3960 . . . 4
43mpteq2dv 4539 . . 3
5 recseq 7062 . . 3
64, 5syl 16 . 2
7 df-rdg 7095 . 2
8 df-rdg 7095 . 2
96, 7, 83eqtr4g 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  rdgsucmpt2  7115  frsucmpt2  7124  seqomlem0  7133  omv  7181  oev  7183  dffi3  7911  hsmex  8833  axdc  8922  seqeq2  12111  seqval  12118  trpredlem1  29310  trpredtr  29313  trpredmintr  29314  neibastop2  30179
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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