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Mirrors > Home > ILE Home > Th. List > reu8 | Unicode version |
Description: Restricted uniqueness using implicit substitution. (Contributed by NM, 24-Oct-2006.) |
Ref | Expression |
---|---|
rmo4.1 |
Ref | Expression |
---|---|
reu8 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rmo4.1 | . . 3 | |
2 | 1 | cbvreuv 2654 | . 2 |
3 | reu6 2868 | . 2 | |
4 | dfbi2 385 | . . . . 5 | |
5 | 4 | ralbii 2439 | . . . 4 |
6 | ancom 264 | . . . . . 6 | |
7 | equcom 1682 | . . . . . . . . . 10 | |
8 | 7 | imbi2i 225 | . . . . . . . . 9 |
9 | 8 | ralbii 2439 | . . . . . . . 8 |
10 | 9 | a1i 9 | . . . . . . 7 |
11 | biimt 240 | . . . . . . . 8 | |
12 | df-ral 2419 | . . . . . . . . 9 | |
13 | bi2.04 247 | . . . . . . . . . 10 | |
14 | 13 | albii 1446 | . . . . . . . . 9 |
15 | vex 2684 | . . . . . . . . . 10 | |
16 | eleq1 2200 | . . . . . . . . . . . . 13 | |
17 | 16, 1 | imbi12d 233 | . . . . . . . . . . . 12 |
18 | 17 | bicomd 140 | . . . . . . . . . . 11 |
19 | 18 | equcoms 1684 | . . . . . . . . . 10 |
20 | 15, 19 | ceqsalv 2711 | . . . . . . . . 9 |
21 | 12, 14, 20 | 3bitrri 206 | . . . . . . . 8 |
22 | 11, 21 | syl6bb 195 | . . . . . . 7 |
23 | 10, 22 | anbi12d 464 | . . . . . 6 |
24 | 6, 23 | syl5bb 191 | . . . . 5 |
25 | r19.26 2556 | . . . . 5 | |
26 | 24, 25 | syl6rbbr 198 | . . . 4 |
27 | 5, 26 | syl5bb 191 | . . 3 |
28 | 27 | rexbiia 2448 | . 2 |
29 | 2, 3, 28 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wcel 1480 wral 2414 wrex 2415 wreu 2416 |
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-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-clab 2124 df-cleq 2130 df-clel 2133 df-ral 2419 df-rex 2420 df-reu 2421 df-v 2683 |
This theorem is referenced by: updjud 6960 |
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