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Mirrors > Home > ILE Home > Th. List > cbvreu | Unicode version |
Description: Change the bound variable of a restricted uniqueness quantifier using implicit substitution. (Contributed by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
cbvral.1 | |
cbvral.2 | |
cbvral.3 |
Ref | Expression |
---|---|
cbvreu |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1461 | . . . 4 | |
2 | 1 | sb8eu 1954 | . . 3 |
3 | sban 1870 | . . . 4 | |
4 | 3 | eubii 1950 | . . 3 |
5 | clelsb3 2183 | . . . . . 6 | |
6 | 5 | anbi1i 445 | . . . . 5 |
7 | 6 | eubii 1950 | . . . 4 |
8 | nfv 1461 | . . . . . 6 | |
9 | cbvral.1 | . . . . . . 7 | |
10 | 9 | nfsb 1863 | . . . . . 6 |
11 | 8, 10 | nfan 1497 | . . . . 5 |
12 | nfv 1461 | . . . . 5 | |
13 | eleq1 2141 | . . . . . 6 | |
14 | sbequ 1761 | . . . . . . 7 | |
15 | cbvral.2 | . . . . . . . 8 | |
16 | cbvral.3 | . . . . . . . 8 | |
17 | 15, 16 | sbie 1714 | . . . . . . 7 |
18 | 14, 17 | syl6bb 194 | . . . . . 6 |
19 | 13, 18 | anbi12d 456 | . . . . 5 |
20 | 11, 12, 19 | cbveu 1965 | . . . 4 |
21 | 7, 20 | bitri 182 | . . 3 |
22 | 2, 4, 21 | 3bitri 204 | . 2 |
23 | df-reu 2355 | . 2 | |
24 | df-reu 2355 | . 2 | |
25 | 22, 23, 24 | 3bitr4i 210 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wnf 1389 wcel 1433 wsb 1685 weu 1941 wreu 2350 |
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-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-cleq 2074 df-clel 2077 df-reu 2355 |
This theorem is referenced by: cbvrmo 2576 cbvreuv 2579 |
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