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Mirrors > Home > NFE Home > Th. List > vtocl2gf | Unicode version |
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 25-Apr-1995.) |
Ref | Expression |
---|---|
vtocl2gf.1 | |
vtocl2gf.2 | |
vtocl2gf.3 | |
vtocl2gf.4 | |
vtocl2gf.5 | |
vtocl2gf.6 | |
vtocl2gf.7 | |
vtocl2gf.8 |
Ref | Expression |
---|---|
vtocl2gf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2867 | . 2 | |
2 | vtocl2gf.3 | . . 3 | |
3 | vtocl2gf.2 | . . . . 5 | |
4 | 3 | nfel1 2499 | . . . 4 |
5 | vtocl2gf.5 | . . . 4 | |
6 | 4, 5 | nfim 1813 | . . 3 |
7 | vtocl2gf.7 | . . . 4 | |
8 | 7 | imbi2d 307 | . . 3 |
9 | vtocl2gf.1 | . . . 4 | |
10 | vtocl2gf.4 | . . . 4 | |
11 | vtocl2gf.6 | . . . 4 | |
12 | vtocl2gf.8 | . . . 4 | |
13 | 9, 10, 11, 12 | vtoclgf 2913 | . . 3 |
14 | 2, 6, 8, 13 | vtoclgf 2913 | . 2 |
15 | 1, 14 | mpan9 455 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wnf 1544 wceq 1642 wcel 1710 wnfc 2476 cvv 2859 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 |
This theorem is referenced by: vtocl3gf 2917 vtocl2g 2918 vtocl2gaf 2921 |
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