Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > vtoclgf | Unicode version |
Description: Implicit substitution of a class for a setvar variable, with bound-variable hypotheses in place of distinct variable restrictions. (Contributed by NM, 21-Sep-2003.) (Proof shortened by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
vtoclgf.1 | |
vtoclgf.2 | |
vtoclgf.3 | |
vtoclgf.4 |
Ref | Expression |
---|---|
vtoclgf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2566 | . 2 | |
2 | vtoclgf.1 | . . . 4 | |
3 | 2 | issetf 2562 | . . 3 |
4 | vtoclgf.2 | . . . 4 | |
5 | vtoclgf.4 | . . . . 5 | |
6 | vtoclgf.3 | . . . . 5 | |
7 | 5, 6 | mpbii 136 | . . . 4 |
8 | 4, 7 | exlimi 1485 | . . 3 |
9 | 3, 8 | sylbi 114 | . 2 |
10 | 1, 9 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wceq 1243 wnf 1349 wex 1381 wcel 1393 wnfc 2165 cvv 2557 |
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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 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-tru 1246 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: vtoclg 2613 vtocl2gf 2615 vtocl3gf 2616 vtoclgaf 2618 ceqsexg 2672 elabgf 2685 mob 2723 opeliunxp2 4476 fvmptss2 5247 |
Copyright terms: Public domain | W3C validator |