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Theorem nfseq 11338
 Description: Hypothesis builder for the sequence builder operation. (Contributed by Mario Carneiro, 24-Jun-2013.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
nfseq.1
nfseq.2
nfseq.3
Assertion
Ref Expression
nfseq

Proof of Theorem nfseq
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-seq 11329 . 2
2 nfcv 2574 . . . . 5
3 nfcv 2574 . . . . . 6
4 nfcv 2574 . . . . . . 7
5 nfseq.2 . . . . . . 7
6 nfseq.3 . . . . . . . 8
76, 3nffv 5738 . . . . . . 7
84, 5, 7nfov 6107 . . . . . 6
93, 8nfop 4002 . . . . 5
102, 2, 9nfmpt2 6145 . . . 4
11 nfseq.1 . . . . 5
126, 11nffv 5738 . . . . 5
1311, 12nfop 4002 . . . 4
1410, 13nfrdg 6675 . . 3
15 nfcv 2574 . . 3
1614, 15nfima 5214 . 2
171, 16nfcxfr 2571 1
 Colors of variables: wff set class Syntax hints:  wnfc 2561  cvv 2958  cop 3819  com 4848  cima 4884  cfv 5457  (class class class)co 6084   cmpt2 6086  crdg 6670  c1 8996   caddc 8998   cseq 11328 This theorem is referenced by:  seqof2  11386  nfsum1  12489  nfsum  12490  lgamgulm2  24825  nfcprod1  25241  nfcprod  25242  fmuldfeqlem1  27702  fmuldfeq  27703  stoweidlem51  27790 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-opab 4270  df-mpt 4271  df-xp 4887  df-cnv 4889  df-dm 4891  df-rn 4892  df-res 4893  df-ima 4894  df-iota 5421  df-fv 5465  df-ov 6087  df-oprab 6088  df-mpt2 6089  df-recs 6636  df-rdg 6671  df-seq 11329
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