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Theorem nfseq 12117
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 12108 . 2
2 nfcv 2619 . . . . 5
3 nfcv 2619 . . . . . 6
4 nfcv 2619 . . . . . . 7
5 nfseq.2 . . . . . . 7
6 nfseq.3 . . . . . . . 8
76, 3nffv 5878 . . . . . . 7
84, 5, 7nfov 6322 . . . . . 6
93, 8nfop 4233 . . . . 5
102, 2, 9nfmpt2 6366 . . . 4
11 nfseq.1 . . . . 5
126, 11nffv 5878 . . . . 5
1311, 12nfop 4233 . . . 4
1410, 13nfrdg 7099 . . 3
15 nfcv 2619 . . 3
1614, 15nfima 5350 . 2
171, 16nfcxfr 2617 1
Colors of variables: wff setvar class
Syntax hints:  F/_wnfc 2605   cvv 3109  <.cop 4035  "cima 5007  `cfv 5593  (class class class)co 6296  e.cmpt2 6298   com 6700  reccrdg 7094  1c1 9514   caddc 9516  seqcseq 12107
This theorem is referenced by:  seqof2  12165  nfsum1  13512  nfsum  13513  nfcprod1  13717  nfcprod  13718  lgamgulm2  28578  binomcxplemdvbinom  31258  binomcxplemdvsum  31260  binomcxplemnotnn0  31261  fmuldfeqlem1  31576  fmuldfeq  31577  sumnnodd  31636  stoweidlem51  31833
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-mpt 4512  df-xp 5010  df-cnv 5012  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017  df-iota 5556  df-fv 5601  df-ov 6299  df-oprab 6300  df-mpt2 6301  df-recs 7061  df-rdg 7095  df-seq 12108
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