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Mirrors > Home > MPE Home > Th. List > vtocl3gf | Structured version Visualization version 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 3212 | . . 3 | |
2 | vtocl3gf.d | . . . 4 | |
3 | vtocl3gf.e | . . . 4 | |
4 | vtocl3gf.f | . . . 4 | |
5 | vtocl3gf.b | . . . . . 6 | |
6 | 5 | nfel1 2779 | . . . . 5 |
7 | vtocl3gf.2 | . . . . 5 | |
8 | 6, 7 | nfim 1825 | . . . 4 |
9 | vtocl3gf.c | . . . . . 6 | |
10 | 9 | nfel1 2779 | . . . . 5 |
11 | vtocl3gf.3 | . . . . 5 | |
12 | 10, 11 | nfim 1825 | . . . 4 |
13 | vtocl3gf.5 | . . . . 5 | |
14 | 13 | imbi2d 330 | . . . 4 |
15 | vtocl3gf.6 | . . . . 5 | |
16 | 15 | imbi2d 330 | . . . 4 |
17 | vtocl3gf.a | . . . . 5 | |
18 | vtocl3gf.1 | . . . . 5 | |
19 | vtocl3gf.4 | . . . . 5 | |
20 | vtocl3gf.7 | . . . . 5 | |
21 | 17, 18, 19, 20 | vtoclgf 3264 | . . . 4 |
22 | 2, 3, 4, 8, 12, 14, 16, 21 | vtocl2gf 3268 | . . 3 |
23 | 1, 22 | mpan9 486 | . 2 |
24 | 23 | 3impb 1260 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wceq 1483 wnf 1708 wcel 1990 wnfc 2751 cvv 3200 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 |
This theorem is referenced by: vtocl3gaf 3275 |
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