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Mirrors > Home > ILE Home > Th. List > vtocl2 | Unicode version |
Description: Implicit substitution of classes for setvar variables. (Contributed by NM, 26-Jul-1995.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) |
Ref | Expression |
---|---|
vtocl2.1 | |
vtocl2.2 | |
vtocl2.3 | |
vtocl2.4 |
Ref | Expression |
---|---|
vtocl2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vtocl2.1 | . . . . . 6 | |
2 | 1 | isseti 2689 | . . . . 5 |
3 | vtocl2.2 | . . . . . 6 | |
4 | 3 | isseti 2689 | . . . . 5 |
5 | eeanv 1902 | . . . . . 6 | |
6 | vtocl2.3 | . . . . . . . 8 | |
7 | 6 | biimpd 143 | . . . . . . 7 |
8 | 7 | 2eximi 1580 | . . . . . 6 |
9 | 5, 8 | sylbir 134 | . . . . 5 |
10 | 2, 4, 9 | mp2an 422 | . . . 4 |
11 | nfv 1508 | . . . . 5 | |
12 | 11 | 19.36-1 1651 | . . . 4 |
13 | 10, 12 | eximii 1581 | . . 3 |
14 | 13 | 19.36aiv 1873 | . 2 |
15 | vtocl2.4 | . . 3 | |
16 | 15 | ax-gen 1425 | . 2 |
17 | 14, 16 | mpg 1427 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wceq 1331 wex 1468 wcel 1480 cvv 2681 |
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 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-v 2683 |
This theorem is referenced by: undifexmid 4112 caovord 5935 ctssexmid 7017 |
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