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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 1930 | . 2 | |
2 | vex 2560 | . . . . . . 7 | |
3 | nfcv 2178 | . . . . . . . 8 | |
4 | nfcsb1v 2882 | . . . . . . . . 9 | |
5 | 4 | nfeq2 2189 | . . . . . . . 8 |
6 | csbeq1a 2860 | . . . . . . . . 9 | |
7 | 6 | eqeq2d 2051 | . . . . . . . 8 |
8 | 3, 5, 7 | spcgf 2635 | . . . . . . 7 |
9 | 2, 8 | ax-mp 7 | . . . . . 6 |
10 | vex 2560 | . . . . . . 7 | |
11 | nfcv 2178 | . . . . . . . 8 | |
12 | nfcsb1v 2882 | . . . . . . . . 9 | |
13 | 12 | nfeq2 2189 | . . . . . . . 8 |
14 | csbeq1a 2860 | . . . . . . . . 9 | |
15 | 14 | eqeq2d 2051 | . . . . . . . 8 |
16 | 11, 13, 15 | spcgf 2635 | . . . . . . 7 |
17 | 10, 16 | ax-mp 7 | . . . . . 6 |
18 | 9, 17 | eqtr3d 2074 | . . . . 5 |
19 | 18 | alrimivv 1755 | . . . 4 |
20 | sbnfc2 2906 | . . . 4 | |
21 | 19, 20 | sylibr 137 | . . 3 |
22 | 21 | exlimiv 1489 | . 2 |
23 | 1, 22 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1241 wceq 1243 wex 1381 wcel 1393 weu 1900 wnfc 2165 cvv 2557 csb 2852 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-sbc 2765 df-csb 2853 |
This theorem is referenced by: eusvnfb 4186 eusv2i 4187 |
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