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Mirrors > Home > ILE Home > Th. List > nfseq | Unicode version |
Description: Hypothesis builder for the sequence builder operation. (Contributed by Mario Carneiro, 24-Jun-2013.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
nfseq.1 | |
nfseq.2 | |
nfseq.3 |
Ref | Expression |
---|---|
nfseq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-seqfrec 10402 | . 2 frec | |
2 | nfcv 2312 | . . . . . 6 | |
3 | nfseq.1 | . . . . . 6 | |
4 | 2, 3 | nffv 5506 | . . . . 5 |
5 | nfcv 2312 | . . . . 5 | |
6 | nfcv 2312 | . . . . . 6 | |
7 | nfcv 2312 | . . . . . . 7 | |
8 | nfseq.2 | . . . . . . 7 | |
9 | nfseq.3 | . . . . . . . 8 | |
10 | 9, 6 | nffv 5506 | . . . . . . 7 |
11 | 7, 8, 10 | nfov 5883 | . . . . . 6 |
12 | 6, 11 | nfop 3781 | . . . . 5 |
13 | 4, 5, 12 | nfmpo 5922 | . . . 4 |
14 | 9, 3 | nffv 5506 | . . . . 5 |
15 | 3, 14 | nfop 3781 | . . . 4 |
16 | 13, 15 | nffrec 6375 | . . 3 frec |
17 | 16 | nfrn 4856 | . 2 frec |
18 | 1, 17 | nfcxfr 2309 | 1 |
Colors of variables: wff set class |
Syntax hints: wnfc 2299 cvv 2730 cop 3586 crn 4612 cfv 5198 (class class class)co 5853 cmpo 5855 freccfrec 6369 c1 7775 caddc 7777 cuz 9487 cseq 10401 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-rab 2457 df-v 2732 df-un 3125 df-in 3127 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-opab 4051 df-mpt 4052 df-xp 4617 df-cnv 4619 df-dm 4621 df-rn 4622 df-res 4623 df-iota 5160 df-fv 5206 df-ov 5856 df-oprab 5857 df-mpo 5858 df-recs 6284 df-frec 6370 df-seqfrec 10402 |
This theorem is referenced by: seq3f1olemstep 10457 seq3f1olemp 10458 nfsum1 11319 nfsum 11320 nfcprod1 11517 nfcprod 11518 |
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