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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 114 | . . 3 |
6 | 3, 5 | alrimi 1502 | . 2 |
7 | vtocld.3 | . . 3 | |
8 | 3, 7 | alrimi 1502 | . 2 |
9 | vtocld.1 | . 2 | |
10 | vtoclgft 2736 | . 2 | |
11 | 1, 2, 6, 8, 9, 10 | syl221anc 1227 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wceq 1331 wnf 1436 wcel 1480 wnfc 2268 |
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 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 |
This theorem is referenced by: vtocld 2738 peano2 4509 iota2df 5112 |
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