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Mirrors > Home > ILE Home > Th. List > nfceqdf | Unicode version |
Description: An equality theorem for effectively not free. (Contributed by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
nfceqdf.1 | |
nfceqdf.2 |
Ref | Expression |
---|---|
nfceqdf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfceqdf.1 | . . . 4 | |
2 | nfceqdf.2 | . . . . 5 | |
3 | 2 | eleq2d 2148 | . . . 4 |
4 | 1, 3 | nfbidf 1472 | . . 3 |
5 | 4 | albidv 1745 | . 2 |
6 | df-nfc 2208 | . 2 | |
7 | df-nfc 2208 | . 2 | |
8 | 5, 6, 7 | 3bitr4g 221 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wal 1282 wceq 1284 wnf 1389 wcel 1433 wnfc 2206 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-17 1459 ax-ial 1467 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-cleq 2074 df-clel 2077 df-nfc 2208 |
This theorem is referenced by: nfopd 3587 dfnfc2 3619 nfimad 4697 nffvd 5207 |
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