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Mirrors > Home > ILE Home > Th. List > vtoclegft | Unicode version |
Description: Implicit substitution of a class for a setvar variable. (Closed theorem version of vtoclef 2785.) (Contributed by NM, 7-Nov-2005.) (Revised by Mario Carneiro, 11-Oct-2016.) |
Ref | Expression |
---|---|
vtoclegft |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2726 | . . . 4 | |
2 | exim 1579 | . . . 4 | |
3 | 1, 2 | mpan9 279 | . . 3 |
4 | 3 | 3adant2 1001 | . 2 |
5 | 19.9t 1622 | . . 3 | |
6 | 5 | 3ad2ant2 1004 | . 2 |
7 | 4, 6 | mpbid 146 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 963 wal 1333 wceq 1335 wnf 1440 wex 1472 wcel 2128 |
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-5 1427 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-v 2714 |
This theorem is referenced by: (None) |
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