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Mirrors > Home > ILE Home > Th. List > vtocl3 | Unicode version |
Description: Implicit substitution of classes for setvar variables. (Contributed by NM, 3-Jun-1995.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) |
Ref | Expression |
---|---|
vtocl3.1 | |
vtocl3.2 | |
vtocl3.3 | |
vtocl3.4 | |
vtocl3.5 |
Ref | Expression |
---|---|
vtocl3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vtocl3.1 | . . . . . . 7 | |
2 | 1 | isseti 2607 | . . . . . 6 |
3 | vtocl3.2 | . . . . . . 7 | |
4 | 3 | isseti 2607 | . . . . . 6 |
5 | vtocl3.3 | . . . . . . 7 | |
6 | 5 | isseti 2607 | . . . . . 6 |
7 | eeeanv 1849 | . . . . . . 7 | |
8 | vtocl3.4 | . . . . . . . . . 10 | |
9 | 8 | biimpd 142 | . . . . . . . . 9 |
10 | 9 | eximi 1531 | . . . . . . . 8 |
11 | 10 | 2eximi 1532 | . . . . . . 7 |
12 | 7, 11 | sylbir 133 | . . . . . 6 |
13 | 2, 4, 6, 12 | mp3an 1268 | . . . . 5 |
14 | nfv 1461 | . . . . . . 7 | |
15 | 14 | 19.36-1 1603 | . . . . . 6 |
16 | 15 | 2eximi 1532 | . . . . 5 |
17 | 13, 16 | ax-mp 7 | . . . 4 |
18 | nfv 1461 | . . . . 5 | |
19 | 18 | 19.36-1 1603 | . . . 4 |
20 | 17, 19 | eximii 1533 | . . 3 |
21 | 20 | 19.36aiv 1822 | . 2 |
22 | vtocl3.5 | . . 3 | |
23 | 22 | gen2 1379 | . 2 |
24 | 21, 23 | mpg 1380 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 w3a 919 wal 1282 wceq 1284 wex 1421 wcel 1433 cvv 2601 |
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-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-v 2603 |
This theorem is referenced by: (None) |
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