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Mirrors > Home > ILE Home > Th. List > abidnf | Unicode version |
Description: Identity used to create closed-form versions of bound-variable hypothesis builders for class expressions. (Contributed by NM, 10-Nov-2005.) (Proof shortened by Mario Carneiro, 12-Oct-2016.) |
Ref | Expression |
---|---|
abidnf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sp 1498 | . . 3 | |
2 | nfcr 2298 | . . . 4 | |
3 | 2 | nfrd 1507 | . . 3 |
4 | 1, 3 | impbid2 142 | . 2 |
5 | 4 | abbi1dv 2284 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1340 wceq 1342 wcel 2135 cab 2150 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-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 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-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 |
This theorem is referenced by: dedhb 2890 nfopd 3769 nfimad 4949 nffvd 5492 |
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