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Theorem nfseq 9932
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  |-  F/_ x M
nfseq.2  |-  F/_ x  .+
nfseq.3  |-  F/_ x F
Assertion
Ref Expression
nfseq  |-  F/_ x  seq M (  .+  ,  F )

Proof of Theorem nfseq
StepHypRef Expression
1 df-seq3 9917 . 2  |-  seq M
(  .+  ,  F
)  =  seq M
(  .+  ,  F ,  _V )
2 nfseq.1 . . 3  |-  F/_ x M
3 nfseq.2 . . 3  |-  F/_ x  .+
4 nfseq.3 . . 3  |-  F/_ x F
5 nfcv 2229 . . 3  |-  F/_ x _V
62, 3, 4, 5nfiseq 9931 . 2  |-  F/_ x  seq M (  .+  ,  F ,  _V )
71, 6nfcxfr 2226 1  |-  F/_ x  seq M (  .+  ,  F )
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2216   _Vcvv 2622    seqcseq4 9914    seqcseq 9915
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071
This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-ral 2365  df-rex 2366  df-rab 2369  df-v 2624  df-un 3006  df-in 3008  df-sn 3458  df-pr 3459  df-op 3461  df-uni 3662  df-br 3854  df-opab 3908  df-mpt 3909  df-xp 4460  df-cnv 4462  df-dm 4464  df-rn 4465  df-res 4466  df-iota 4995  df-fv 5038  df-ov 5671  df-oprab 5672  df-mpt2 5673  df-recs 6086  df-frec 6172  df-iseq 9916  df-seq3 9917
This theorem is referenced by:  seq3f1olemstep  9993  seq3f1olemp  9994
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