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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 2738 | . . . . . 6 |
3 | vtocl3.2 | . . . . . . 7 | |
4 | 3 | isseti 2738 | . . . . . 6 |
5 | vtocl3.3 | . . . . . . 7 | |
6 | 5 | isseti 2738 | . . . . . 6 |
7 | eeeanv 1926 | . . . . . . 7 | |
8 | vtocl3.4 | . . . . . . . . . 10 | |
9 | 8 | biimpd 143 | . . . . . . . . 9 |
10 | 9 | eximi 1593 | . . . . . . . 8 |
11 | 10 | 2eximi 1594 | . . . . . . 7 |
12 | 7, 11 | sylbir 134 | . . . . . 6 |
13 | 2, 4, 6, 12 | mp3an 1332 | . . . . 5 |
14 | nfv 1521 | . . . . . . 7 | |
15 | 14 | 19.36-1 1666 | . . . . . 6 |
16 | 15 | 2eximi 1594 | . . . . 5 |
17 | 13, 16 | ax-mp 5 | . . . 4 |
18 | nfv 1521 | . . . . 5 | |
19 | 18 | 19.36-1 1666 | . . . 4 |
20 | 17, 19 | eximii 1595 | . . 3 |
21 | 20 | 19.36aiv 1894 | . 2 |
22 | vtocl3.5 | . . 3 | |
23 | 22 | gen2 1443 | . 2 |
24 | 21, 23 | mpg 1444 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 973 wal 1346 wceq 1348 wex 1485 wcel 2141 cvv 2730 |
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-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-v 2732 |
This theorem is referenced by: (None) |
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