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Mirrors > Home > ILE Home > Th. List > riota2df | Unicode version |
Description: A deduction version of riota2f 5744. (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 274 | . . 3 |
3 | simpr 109 | . . . 4 | |
4 | df-reu 2421 | . . . 4 | |
5 | 3, 4 | sylib 121 | . . 3 |
6 | simpr 109 | . . . . . 6 | |
7 | 2 | adantr 274 | . . . . . 6 |
8 | 6, 7 | eqeltrd 2214 | . . . . 5 |
9 | 8 | biantrurd 303 | . . . 4 |
10 | riota2df.5 | . . . . 5 | |
11 | 10 | adantlr 468 | . . . 4 |
12 | 9, 11 | bitr3d 189 | . . 3 |
13 | riota2df.1 | . . . 4 | |
14 | nfreu1 2600 | . . . 4 | |
15 | 13, 14 | nfan 1544 | . . 3 |
16 | riota2df.3 | . . . 4 | |
17 | 16 | adantr 274 | . . 3 |
18 | riota2df.2 | . . . 4 | |
19 | 18 | adantr 274 | . . 3 |
20 | 2, 5, 12, 15, 17, 19 | iota2df 5107 | . 2 |
21 | df-riota 5723 | . . 3 | |
22 | 21 | eqeq1i 2145 | . 2 |
23 | 20, 22 | syl6bbr 197 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wnf 1436 wcel 1480 weu 1997 wnfc 2266 wreu 2416 cio 5081 crio 5722 |
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 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-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rex 2420 df-reu 2421 df-v 2683 df-sbc 2905 df-un 3070 df-sn 3528 df-pr 3529 df-uni 3732 df-iota 5083 df-riota 5723 |
This theorem is referenced by: riota2f 5744 riota5f 5747 |
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