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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 1488 | . . 3 | |
2 | nfcr 2271 | . . . 4 | |
3 | 2 | nfrd 1500 | . . 3 |
4 | 1, 3 | impbid2 142 | . 2 |
5 | 4 | abbi1dv 2257 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1329 wceq 1331 wcel 1480 cab 2123 wnfc 2266 |
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-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 |
This theorem is referenced by: dedhb 2848 nfopd 3717 nfimad 4885 nffvd 5426 |
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