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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 2027 | . 2 | |
2 | vex 2684 | . . . . . . 7 | |
3 | nfcv 2279 | . . . . . . . 8 | |
4 | nfcsb1v 3030 | . . . . . . . . 9 | |
5 | 4 | nfeq2 2291 | . . . . . . . 8 |
6 | csbeq1a 3007 | . . . . . . . . 9 | |
7 | 6 | eqeq2d 2149 | . . . . . . . 8 |
8 | 3, 5, 7 | spcgf 2763 | . . . . . . 7 |
9 | 2, 8 | ax-mp 5 | . . . . . 6 |
10 | vex 2684 | . . . . . . 7 | |
11 | nfcv 2279 | . . . . . . . 8 | |
12 | nfcsb1v 3030 | . . . . . . . . 9 | |
13 | 12 | nfeq2 2291 | . . . . . . . 8 |
14 | csbeq1a 3007 | . . . . . . . . 9 | |
15 | 14 | eqeq2d 2149 | . . . . . . . 8 |
16 | 11, 13, 15 | spcgf 2763 | . . . . . . 7 |
17 | 10, 16 | ax-mp 5 | . . . . . 6 |
18 | 9, 17 | eqtr3d 2172 | . . . . 5 |
19 | 18 | alrimivv 1847 | . . . 4 |
20 | sbnfc2 3055 | . . . 4 | |
21 | 19, 20 | sylibr 133 | . . 3 |
22 | 21 | exlimiv 1577 | . 2 |
23 | 1, 22 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1329 wceq 1331 wex 1468 wcel 1480 weu 1997 wnfc 2266 cvv 2681 csb 2998 |
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-nfc 2268 df-v 2683 df-sbc 2905 df-csb 2999 |
This theorem is referenced by: eusvnfb 4370 eusv2i 4371 |
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