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Theorem nfiseq 9218
 Description: Hypothesis builder for the sequence builder operation. (Contributed by Jim Kingdon, 30-May-2020.)
Hypotheses
Ref Expression
nfiseq.1
nfiseq.2
nfiseq.3
nfiseq.4
Assertion
Ref Expression
nfiseq

Proof of Theorem nfiseq
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-iseq 9212 . 2 frec
2 nfcv 2178 . . . . . 6
3 nfiseq.1 . . . . . 6
42, 3nffv 5185 . . . . 5
5 nfiseq.4 . . . . 5
6 nfcv 2178 . . . . . 6
7 nfcv 2178 . . . . . . 7
8 nfiseq.2 . . . . . . 7
9 nfiseq.3 . . . . . . . 8
109, 6nffv 5185 . . . . . . 7
117, 8, 10nfov 5535 . . . . . 6
126, 11nfop 3565 . . . . 5
134, 5, 12nfmpt2 5573 . . . 4
149, 3nffv 5185 . . . . 5
153, 14nfop 3565 . . . 4
1613, 15nffrec 5982 . . 3 frec
1716nfrn 4579 . 2 frec
181, 17nfcxfr 2175 1
 Colors of variables: wff set class Syntax hints:  wnfc 2165  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-rab 2315  df-v 2559  df-un 2922  df-in 2924  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-opab 3819  df-mpt 3820  df-xp 4351  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:  nfsum1  9875  nfsum  9876
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