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Theorem rdgeq1 7074
 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 5863 . . . . . 6
21ifeq2d 3958 . . . . 5
32ifeq2d 3958 . . . 4
43mpteq2dv 4534 . . 3
5 recseq 7040 . . 3 recs recs
64, 5syl 16 . 2 recs recs
7 df-rdg 7073 . 2 recs
8 df-rdg 7073 . 2 recs
96, 7, 83eqtr4g 2533 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1379  cvv 3113  c0 3785  cif 3939  cuni 4245   cmpt 4505   wlim 4879   cdm 4999   crn 5000  cfv 5586  recscrecs 7038  crdg 7072 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-un 3481  df-if 3940  df-uni 4246  df-br 4448  df-opab 4506  df-mpt 4507  df-iota 5549  df-fv 5594  df-recs 7039  df-rdg 7073 This theorem is referenced by:  rdgeq12  7076  rdgsucmpt2  7093  frsucmpt2  7102  seqomlem0  7111  omv  7159  oev  7161  dffi3  7887  hsmex  8808  axdc  8897  seqeq2  12074  seqval  12081  trpredlem1  28884  trpredtr  28887  trpredmintr  28888  neibastop2  29780
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