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Mirrors > Home > ILE Home > Th. List > vtocldf | Unicode version |
Description: Implicit substitution of a class for a setvar variable. (Contributed by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
vtocld.1 | |
vtocld.2 | |
vtocld.3 | |
vtocldf.4 | |
vtocldf.5 | |
vtocldf.6 |
Ref | Expression |
---|---|
vtocldf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vtocldf.5 | . 2 | |
2 | vtocldf.6 | . 2 | |
3 | vtocldf.4 | . . 3 | |
4 | vtocld.2 | . . . 4 | |
5 | 4 | ex 108 | . . 3 |
6 | 3, 5 | alrimi 1415 | . 2 |
7 | vtocld.3 | . . 3 | |
8 | 3, 7 | alrimi 1415 | . 2 |
9 | vtocld.1 | . 2 | |
10 | vtoclgft 2604 | . 2 | |
11 | 1, 2, 6, 8, 9, 10 | syl221anc 1146 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wnf 1349 wcel 1393 wnfc 2165 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 |
This theorem is referenced by: vtocld 2606 peano2 4318 iota2df 4891 |
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