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Mirrors > Home > ILE Home > Th. List > reu6 | Unicode version |
Description: A way to express restricted uniqueness. (Contributed by NM, 20-Oct-2006.) |
Ref | Expression |
---|---|
reu6 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-reu 2449 | . 2 | |
2 | 19.28v 1887 | . . . . 5 | |
3 | eleq1 2227 | . . . . . . . . . . . 12 | |
4 | sbequ12 1758 | . . . . . . . . . . . 12 | |
5 | 3, 4 | anbi12d 465 | . . . . . . . . . . 11 |
6 | equequ1 1699 | . . . . . . . . . . 11 | |
7 | 5, 6 | bibi12d 234 | . . . . . . . . . 10 |
8 | equid 1688 | . . . . . . . . . . . 12 | |
9 | 8 | tbt 246 | . . . . . . . . . . 11 |
10 | simpl 108 | . . . . . . . . . . 11 | |
11 | 9, 10 | sylbir 134 | . . . . . . . . . 10 |
12 | 7, 11 | syl6bi 162 | . . . . . . . . 9 |
13 | 12 | spimv 1798 | . . . . . . . 8 |
14 | biimp 117 | . . . . . . . . . . . 12 | |
15 | 14 | expdimp 257 | . . . . . . . . . . 11 |
16 | biimpr 129 | . . . . . . . . . . . . 13 | |
17 | simpr 109 | . . . . . . . . . . . . 13 | |
18 | 16, 17 | syl6 33 | . . . . . . . . . . . 12 |
19 | 18 | adantr 274 | . . . . . . . . . . 11 |
20 | 15, 19 | impbid 128 | . . . . . . . . . 10 |
21 | 20 | ex 114 | . . . . . . . . 9 |
22 | 21 | sps 1524 | . . . . . . . 8 |
23 | 13, 22 | jca 304 | . . . . . . 7 |
24 | 23 | a5i 1530 | . . . . . 6 |
25 | biimp 117 | . . . . . . . . . . 11 | |
26 | 25 | imim2i 12 | . . . . . . . . . 10 |
27 | 26 | impd 252 | . . . . . . . . 9 |
28 | 27 | adantl 275 | . . . . . . . 8 |
29 | eleq1a 2236 | . . . . . . . . . . . 12 | |
30 | 29 | adantr 274 | . . . . . . . . . . 11 |
31 | 30 | imp 123 | . . . . . . . . . 10 |
32 | biimpr 129 | . . . . . . . . . . . . . 14 | |
33 | 32 | imim2i 12 | . . . . . . . . . . . . 13 |
34 | 33 | com23 78 | . . . . . . . . . . . 12 |
35 | 34 | imp 123 | . . . . . . . . . . 11 |
36 | 35 | adantll 468 | . . . . . . . . . 10 |
37 | 31, 36 | jcai 309 | . . . . . . . . 9 |
38 | 37 | ex 114 | . . . . . . . 8 |
39 | 28, 38 | impbid 128 | . . . . . . 7 |
40 | 39 | alimi 1442 | . . . . . 6 |
41 | 24, 40 | impbii 125 | . . . . 5 |
42 | df-ral 2447 | . . . . . 6 | |
43 | 42 | anbi2i 453 | . . . . 5 |
44 | 2, 41, 43 | 3bitr4i 211 | . . . 4 |
45 | 44 | exbii 1592 | . . 3 |
46 | df-eu 2016 | . . 3 | |
47 | df-rex 2448 | . . 3 | |
48 | 45, 46, 47 | 3bitr4i 211 | . 2 |
49 | 1, 48 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1340 wex 1479 wsb 1749 weu 2013 wcel 2135 wral 2442 wrex 2443 wreu 2444 |
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-5 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-eu 2016 df-cleq 2157 df-clel 2160 df-ral 2447 df-rex 2448 df-reu 2449 |
This theorem is referenced by: reu3 2911 reu6i 2912 reu8 2917 xpf1o 6801 |
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