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Theorem rdgeq2 6425
 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 3569 . . . 4
21mpteq2dv 4107 . . 3
3 recseq 6389 . . 3 recs recs
42, 3syl 15 . 2 recs recs
5 df-rdg 6423 . 2 recs
6 df-rdg 6423 . 2 recs
74, 5, 63eqtr4g 2340 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1623  cvv 2788  c0 3455  cif 3565  cuni 3827   cmpt 4077   wlim 4393   cdm 4689   crn 4690  cfv 5255  recscrecs 6387  crdg 6422 This theorem is referenced by:  rdgeq12  6426  rdg0g  6440  oav  6510  itunifval  8042  hsmex  8058  ltweuz  11024  seqeq1  11049  dfrdg2  24152  trpredeq3  24225  valtar  25883  trclval  25894 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-un 3157  df-if 3566  df-uni 3828  df-br 4024  df-opab 4078  df-mpt 4079  df-iota 5219  df-fv 5263  df-recs 6388  df-rdg 6423
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