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Mirrors > Home > ILE Home > Th. List > riota2df | Unicode version |
Description: A deduction version of riota2f 5509. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
riota2df.1 | |
riota2df.2 | |
riota2df.3 | |
riota2df.4 | |
riota2df.5 |
Ref | Expression |
---|---|
riota2df |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | riota2df.4 | . . . 4 | |
2 | 1 | adantr 270 | . . 3 |
3 | simpr 108 | . . . 4 | |
4 | df-reu 2355 | . . . 4 | |
5 | 3, 4 | sylib 120 | . . 3 |
6 | simpr 108 | . . . . . 6 | |
7 | 2 | adantr 270 | . . . . . 6 |
8 | 6, 7 | eqeltrd 2155 | . . . . 5 |
9 | 8 | biantrurd 299 | . . . 4 |
10 | riota2df.5 | . . . . 5 | |
11 | 10 | adantlr 460 | . . . 4 |
12 | 9, 11 | bitr3d 188 | . . 3 |
13 | riota2df.1 | . . . 4 | |
14 | nfreu1 2525 | . . . 4 | |
15 | 13, 14 | nfan 1497 | . . 3 |
16 | riota2df.3 | . . . 4 | |
17 | 16 | adantr 270 | . . 3 |
18 | riota2df.2 | . . . 4 | |
19 | 18 | adantr 270 | . . 3 |
20 | 2, 5, 12, 15, 17, 19 | iota2df 4911 | . 2 |
21 | df-riota 5488 | . . 3 | |
22 | 21 | eqeq1i 2088 | . 2 |
23 | 20, 22 | syl6bbr 196 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wnf 1389 wcel 1433 weu 1941 wnfc 2206 wreu 2350 cio 4885 crio 5487 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rex 2354 df-reu 2355 df-v 2603 df-sbc 2816 df-un 2977 df-sn 3404 df-pr 3405 df-uni 3602 df-iota 4887 df-riota 5488 |
This theorem is referenced by: riota2f 5509 riota5f 5512 |
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