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Mirrors > Home > ILE Home > Th. List > ceqsexg | Unicode version |
Description: A representation of explicit substitution of a class for a variable, inferred from an implicit substitution hypothesis. (Contributed by NM, 11-Oct-2004.) |
Ref | Expression |
---|---|
ceqsexg.1 | |
ceqsexg.2 |
Ref | Expression |
---|---|
ceqsexg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2178 | . 2 | |
2 | nfe1 1385 | . . 3 | |
3 | ceqsexg.1 | . . 3 | |
4 | 2, 3 | nfbi 1481 | . 2 |
5 | ceqex 2671 | . . 3 | |
6 | ceqsexg.2 | . . 3 | |
7 | 5, 6 | bibi12d 224 | . 2 |
8 | biid 160 | . 2 | |
9 | 1, 4, 7, 8 | vtoclgf 2612 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wnf 1349 wex 1381 wcel 1393 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 |
This theorem is referenced by: ceqsexgv 2673 |
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