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Mirrors > Home > ILE Home > Th. List > vtoclgaf | Unicode version |
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 17-Feb-2006.) (Revised by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
vtoclgaf.1 | |
vtoclgaf.2 | |
vtoclgaf.3 | |
vtoclgaf.4 |
Ref | Expression |
---|---|
vtoclgaf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vtoclgaf.1 | . . 3 | |
2 | 1 | nfel1 2292 | . . . 4 |
3 | vtoclgaf.2 | . . . 4 | |
4 | 2, 3 | nfim 1551 | . . 3 |
5 | eleq1 2202 | . . . 4 | |
6 | vtoclgaf.3 | . . . 4 | |
7 | 5, 6 | imbi12d 233 | . . 3 |
8 | vtoclgaf.4 | . . 3 | |
9 | 1, 4, 7, 8 | vtoclgf 2744 | . 2 |
10 | 9 | pm2.43i 49 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 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-tru 1334 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: vtoclga 2752 ssiun2s 3857 tfis 4497 fvmptf 5513 fmptco 5586 prmind2 11801 |
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