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Mirrors > Home > ILE Home > Th. List > nfsum1 | Unicode version |
Description: Bound-variable hypothesis builder for sum. (Contributed by NM, 11-Dec-2005.) (Revised by Mario Carneiro, 13-Jun-2019.) |
Ref | Expression |
---|---|
nfsum1.1 |
Ref | Expression |
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nfsum1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-sumdc 11116 | . 2 DECID | |
2 | nfcv 2279 | . . . . 5 | |
3 | nfsum1.1 | . . . . . . 7 | |
4 | nfcv 2279 | . . . . . . 7 | |
5 | 3, 4 | nfss 3085 | . . . . . 6 |
6 | 3 | nfcri 2273 | . . . . . . . 8 |
7 | 6 | nfdc 1637 | . . . . . . 7 DECID |
8 | 4, 7 | nfralxy 2469 | . . . . . 6 DECID |
9 | nfcv 2279 | . . . . . . . 8 | |
10 | nfcv 2279 | . . . . . . . 8 | |
11 | 3 | nfcri 2273 | . . . . . . . . . 10 |
12 | nfcsb1v 3030 | . . . . . . . . . 10 | |
13 | nfcv 2279 | . . . . . . . . . 10 | |
14 | 11, 12, 13 | nfif 3495 | . . . . . . . . 9 |
15 | 2, 14 | nfmpt 4015 | . . . . . . . 8 |
16 | 9, 10, 15 | nfseq 10221 | . . . . . . 7 |
17 | nfcv 2279 | . . . . . . 7 | |
18 | nfcv 2279 | . . . . . . 7 | |
19 | 16, 17, 18 | nfbr 3969 | . . . . . 6 |
20 | 5, 8, 19 | nf3an 1545 | . . . . 5 DECID |
21 | 2, 20 | nfrexya 2472 | . . . 4 DECID |
22 | nfcv 2279 | . . . . 5 | |
23 | nfcv 2279 | . . . . . . . 8 | |
24 | nfcv 2279 | . . . . . . . 8 | |
25 | 23, 24, 3 | nff1o 5358 | . . . . . . 7 |
26 | nfcv 2279 | . . . . . . . . . 10 | |
27 | nfv 1508 | . . . . . . . . . . . 12 | |
28 | nfcsb1v 3030 | . . . . . . . . . . . 12 | |
29 | 27, 28, 13 | nfif 3495 | . . . . . . . . . . 11 |
30 | 22, 29 | nfmpt 4015 | . . . . . . . . . 10 |
31 | 26, 10, 30 | nfseq 10221 | . . . . . . . . 9 |
32 | 31, 9 | nffv 5424 | . . . . . . . 8 |
33 | 32 | nfeq2 2291 | . . . . . . 7 |
34 | 25, 33 | nfan 1544 | . . . . . 6 |
35 | 34 | nfex 1616 | . . . . 5 |
36 | 22, 35 | nfrexya 2472 | . . . 4 |
37 | 21, 36 | nfor 1553 | . . 3 DECID |
38 | 37 | nfiotaw 5087 | . 2 DECID |
39 | 1, 38 | nfcxfr 2276 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wo 697 DECID wdc 819 w3a 962 wceq 1331 wex 1468 wcel 1480 wnfc 2266 wral 2414 wrex 2415 csb 2998 wss 3066 cif 3469 class class class wbr 3924 cmpt 3984 cio 5081 wf1o 5117 cfv 5118 (class class class)co 5767 cc0 7613 c1 7614 caddc 7616 cle 7794 cn 8713 cz 9047 cuz 9319 cfz 9783 cseq 10211 cli 11040 csu 11115 |
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-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-dc 820 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-sbc 2905 df-csb 2999 df-un 3070 df-in 3072 df-ss 3079 df-if 3470 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-mpt 3986 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-res 4546 df-iota 5083 df-fun 5120 df-fn 5121 df-f 5122 df-f1 5123 df-fo 5124 df-f1o 5125 df-fv 5126 df-ov 5770 df-oprab 5771 df-mpo 5772 df-recs 6195 df-frec 6281 df-seqfrec 10212 df-sumdc 11116 |
This theorem is referenced by: mertenslem2 11298 |
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