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Mirrors > Home > ILE Home > Th. List > riota5f | Unicode version |
Description: A method for computing restricted iota. (Contributed by NM, 16-Apr-2013.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
riota5f.1 | |
riota5f.2 | |
riota5f.3 |
Ref | Expression |
---|---|
riota5f |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | riota5f.3 | . . 3 | |
2 | 1 | ralrimiva 2537 | . 2 |
3 | riota5f.2 | . . . 4 | |
4 | a1tru 1358 | . . . . . . 7 | |
5 | reu6i 2912 | . . . . . . . . 9 | |
6 | 5 | adantl 275 | . . . . . . . 8 |
7 | nfv 1515 | . . . . . . . . . 10 | |
8 | nfv 1515 | . . . . . . . . . . 11 | |
9 | nfra1 2495 | . . . . . . . . . . 11 | |
10 | 8, 9 | nfan 1552 | . . . . . . . . . 10 |
11 | 7, 10 | nfan 1552 | . . . . . . . . 9 |
12 | nfcvd 2307 | . . . . . . . . 9 | |
13 | nfvd 1516 | . . . . . . . . 9 | |
14 | simprl 521 | . . . . . . . . 9 | |
15 | simpr 109 | . . . . . . . . . . 11 | |
16 | simplrr 526 | . . . . . . . . . . . 12 | |
17 | simplrl 525 | . . . . . . . . . . . . 13 | |
18 | 15, 17 | eqeltrd 2241 | . . . . . . . . . . . 12 |
19 | rsp 2511 | . . . . . . . . . . . 12 | |
20 | 16, 18, 19 | sylc 62 | . . . . . . . . . . 11 |
21 | 15, 20 | mpbird 166 | . . . . . . . . . 10 |
22 | a1tru 1358 | . . . . . . . . . 10 | |
23 | 21, 22 | 2thd 174 | . . . . . . . . 9 |
24 | 11, 12, 13, 14, 23 | riota2df 5812 | . . . . . . . 8 |
25 | 6, 24 | mpdan 418 | . . . . . . 7 |
26 | 4, 25 | mpbid 146 | . . . . . 6 |
27 | 26 | expr 373 | . . . . 5 |
28 | 27 | ralrimiva 2537 | . . . 4 |
29 | rspsbc 3028 | . . . 4 | |
30 | 3, 28, 29 | sylc 62 | . . 3 |
31 | nfcvd 2307 | . . . . . . . 8 | |
32 | riota5f.1 | . . . . . . . 8 | |
33 | 31, 32 | nfeqd 2321 | . . . . . . 7 |
34 | 7, 33 | nfan1 1551 | . . . . . 6 |
35 | simpr 109 | . . . . . . . 8 | |
36 | 35 | eqeq2d 2176 | . . . . . . 7 |
37 | 36 | bibi2d 231 | . . . . . 6 |
38 | 34, 37 | ralbid 2462 | . . . . 5 |
39 | 35 | eqeq2d 2176 | . . . . 5 |
40 | 38, 39 | imbi12d 233 | . . . 4 |
41 | 3, 40 | sbcied 2982 | . . 3 |
42 | 30, 41 | mpbid 146 | . 2 |
43 | 2, 42 | mpd 13 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1342 wtru 1343 wcel 2135 wnfc 2293 wral 2442 wreu 2444 wsbc 2946 crio 5791 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-reu 2449 df-v 2723 df-sbc 2947 df-un 3115 df-sn 3576 df-pr 3577 df-uni 3784 df-iota 5147 df-riota 5792 |
This theorem is referenced by: riota5 5817 |
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