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Mirrors > Home > ILE Home > Th. List > eusvnf | Unicode version |
Description: Even if is free in , it is effectively bound when is single-valued. (Contributed by NM, 14-Oct-2010.) (Revised by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
eusvnf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euex 1971 | . 2 | |
2 | vex 2604 | . . . . . . 7 | |
3 | nfcv 2219 | . . . . . . . 8 | |
4 | nfcsb1v 2938 | . . . . . . . . 9 | |
5 | 4 | nfeq2 2230 | . . . . . . . 8 |
6 | csbeq1a 2916 | . . . . . . . . 9 | |
7 | 6 | eqeq2d 2092 | . . . . . . . 8 |
8 | 3, 5, 7 | spcgf 2680 | . . . . . . 7 |
9 | 2, 8 | ax-mp 7 | . . . . . 6 |
10 | vex 2604 | . . . . . . 7 | |
11 | nfcv 2219 | . . . . . . . 8 | |
12 | nfcsb1v 2938 | . . . . . . . . 9 | |
13 | 12 | nfeq2 2230 | . . . . . . . 8 |
14 | csbeq1a 2916 | . . . . . . . . 9 | |
15 | 14 | eqeq2d 2092 | . . . . . . . 8 |
16 | 11, 13, 15 | spcgf 2680 | . . . . . . 7 |
17 | 10, 16 | ax-mp 7 | . . . . . 6 |
18 | 9, 17 | eqtr3d 2115 | . . . . 5 |
19 | 18 | alrimivv 1796 | . . . 4 |
20 | sbnfc2 2962 | . . . 4 | |
21 | 19, 20 | sylibr 132 | . . 3 |
22 | 21 | exlimiv 1529 | . 2 |
23 | 1, 22 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1282 wceq 1284 wex 1421 wcel 1433 weu 1941 wnfc 2206 cvv 2601 csb 2908 |
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-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-sbc 2816 df-csb 2909 |
This theorem is referenced by: eusvnfb 4204 eusv2i 4205 |
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