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Theorem iseqeq2 9215
 Description: Equality theorem for the sequence builder operation. (Contributed by Jim Kingdon, 30-May-2020.)
Assertion
Ref Expression
iseqeq2

Proof of Theorem iseqeq2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 simp1 904 . . . . . . 7
21oveqd 5529 . . . . . 6
32opeq2d 3556 . . . . 5
43mpt2eq3dva 5569 . . . 4
5 freceq1 5979 . . . 4 frec frec
64, 5syl 14 . . 3 frec frec
76rneqd 4563 . 2 frec frec
8 df-iseq 9212 . 2 frec
9 df-iseq 9212 . 2 frec
107, 8, 93eqtr4g 2097 1
 Colors of variables: wff set class Syntax hints:   wi 4   w3a 885   wceq 1243   wcel 1393  cop 3378   crn 4346  cfv 4902  (class class class)co 5512   cmpt2 5514  freccfrec 5977  c1 6890   caddc 6892  cuz 8473   cseq 9211 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-opab 3819  df-mpt 3820  df-cnv 4353  df-dm 4355  df-rn 4356  df-res 4357  df-iota 4867  df-fv 4910  df-ov 5515  df-oprab 5516  df-mpt2 5517  df-recs 5920  df-frec 5978  df-iseq 9212 This theorem is referenced by:  resqrex  9624
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