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Mirrors > Home > ILE Home > Th. List > vtocl3gf | Unicode version |
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 10-Aug-2013.) (Revised by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
vtocl3gf.a | |
vtocl3gf.b | |
vtocl3gf.c | |
vtocl3gf.d | |
vtocl3gf.e | |
vtocl3gf.f | |
vtocl3gf.1 | |
vtocl3gf.2 | |
vtocl3gf.3 | |
vtocl3gf.4 | |
vtocl3gf.5 | |
vtocl3gf.6 | |
vtocl3gf.7 |
Ref | Expression |
---|---|
vtocl3gf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2697 | . . 3 | |
2 | vtocl3gf.d | . . . 4 | |
3 | vtocl3gf.e | . . . 4 | |
4 | vtocl3gf.f | . . . 4 | |
5 | vtocl3gf.b | . . . . . 6 | |
6 | 5 | nfel1 2292 | . . . . 5 |
7 | vtocl3gf.2 | . . . . 5 | |
8 | 6, 7 | nfim 1551 | . . . 4 |
9 | vtocl3gf.c | . . . . . 6 | |
10 | 9 | nfel1 2292 | . . . . 5 |
11 | vtocl3gf.3 | . . . . 5 | |
12 | 10, 11 | nfim 1551 | . . . 4 |
13 | vtocl3gf.5 | . . . . 5 | |
14 | 13 | imbi2d 229 | . . . 4 |
15 | vtocl3gf.6 | . . . . 5 | |
16 | 15 | imbi2d 229 | . . . 4 |
17 | vtocl3gf.a | . . . . 5 | |
18 | vtocl3gf.1 | . . . . 5 | |
19 | vtocl3gf.4 | . . . . 5 | |
20 | vtocl3gf.7 | . . . . 5 | |
21 | 17, 18, 19, 20 | vtoclgf 2744 | . . . 4 |
22 | 2, 3, 4, 8, 12, 14, 16, 21 | vtocl2gf 2748 | . . 3 |
23 | 1, 22 | mpan9 279 | . 2 |
24 | 23 | 3impb 1177 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 962 wceq 1331 wnf 1436 wcel 1480 wnfc 2268 cvv 2686 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 |
This theorem is referenced by: vtocl3gaf 2755 |
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