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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 2317 | . . . 4 |
3 | vtoclgaf.2 | . . . 4 | |
4 | 2, 3 | nfim 1559 | . . 3 |
5 | eleq1 2227 | . . . 4 | |
6 | vtoclgaf.3 | . . . 4 | |
7 | 5, 6 | imbi12d 233 | . . 3 |
8 | vtoclgaf.4 | . . 3 | |
9 | 1, 4, 7, 8 | vtoclgf 2779 | . 2 |
10 | 9 | pm2.43i 49 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1342 wnf 1447 wcel 2135 wnfc 2293 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 |
This theorem is referenced by: vtoclga 2787 ssiun2s 3904 tfis 4554 fvmptf 5572 fmptco 5645 prmind2 12031 |
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