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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 10187 | . 2 frec | |
2 | nfcv 2258 | . . . . . 6 | |
3 | nfseq.1 | . . . . . 6 | |
4 | 2, 3 | nffv 5399 | . . . . 5 |
5 | nfcv 2258 | . . . . 5 | |
6 | nfcv 2258 | . . . . . 6 | |
7 | nfcv 2258 | . . . . . . 7 | |
8 | nfseq.2 | . . . . . . 7 | |
9 | nfseq.3 | . . . . . . . 8 | |
10 | 9, 6 | nffv 5399 | . . . . . . 7 |
11 | 7, 8, 10 | nfov 5769 | . . . . . 6 |
12 | 6, 11 | nfop 3691 | . . . . 5 |
13 | 4, 5, 12 | nfmpo 5808 | . . . 4 |
14 | 9, 3 | nffv 5399 | . . . . 5 |
15 | 3, 14 | nfop 3691 | . . . 4 |
16 | 13, 15 | nffrec 6261 | . . 3 frec |
17 | 16 | nfrn 4754 | . 2 frec |
18 | 1, 17 | nfcxfr 2255 | 1 |
Colors of variables: wff set class |
Syntax hints: wnfc 2245 cvv 2660 cop 3500 crn 4510 cfv 5093 (class class class)co 5742 cmpo 5744 freccfrec 6255 c1 7589 caddc 7591 cuz 9294 cseq 10186 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-rab 2402 df-v 2662 df-un 3045 df-in 3047 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-mpt 3961 df-xp 4515 df-cnv 4517 df-dm 4519 df-rn 4520 df-res 4521 df-iota 5058 df-fv 5101 df-ov 5745 df-oprab 5746 df-mpo 5747 df-recs 6170 df-frec 6256 df-seqfrec 10187 |
This theorem is referenced by: seq3f1olemstep 10242 seq3f1olemp 10243 nfsum1 11093 nfsum 11094 |
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