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Mirrors > Home > NFE 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 2867 | . 2 | |
2 | vtoclgf.1 | . . . 4 | |
3 | 2 | issetf 2864 | . . 3 |
4 | vtoclgf.2 | . . . 4 | |
5 | vtoclgf.4 | . . . . 5 | |
6 | vtoclgf.3 | . . . . 5 | |
7 | 5, 6 | mpbii 202 | . . . 4 |
8 | 4, 7 | exlimi 1803 | . . 3 |
9 | 3, 8 | sylbi 187 | . 2 |
10 | 1, 9 | syl 15 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wex 1541 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: vtoclg 2914 vtocl2gf 2916 vtocl3gf 2917 vtoclgaf 2919 ceqsexg 2970 elabgf 2983 mob 3018 opeliunxp2 4822 |
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