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Mirrors > Home > ILE Home > Th. List > nfeld | Unicode version |
Description: Hypothesis builder for elementhood. (Contributed by Mario Carneiro, 7-Oct-2016.) |
Ref | Expression |
---|---|
nfeqd.1 | |
nfeqd.2 |
Ref | Expression |
---|---|
nfeld |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-clel 2036 | . 2 | |
2 | nfv 1421 | . . 3 | |
3 | nfcvd 2179 | . . . . 5 | |
4 | nfeqd.1 | . . . . 5 | |
5 | 3, 4 | nfeqd 2192 | . . . 4 |
6 | nfeqd.2 | . . . . 5 | |
7 | 6 | nfcrd 2191 | . . . 4 |
8 | 5, 7 | nfand 1460 | . . 3 |
9 | 2, 8 | nfexd 1644 | . 2 |
10 | 1, 9 | nfxfrd 1364 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wceq 1243 wnf 1349 wex 1381 wcel 1393 wnfc 2165 |
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-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-cleq 2033 df-clel 2036 df-nfc 2167 |
This theorem is referenced by: nfneld 2305 nfraldxy 2356 nfrexdxy 2357 nfreudxy 2483 nfsbc1d 2780 nfsbcd 2783 sbcrext 2835 nfbrd 3807 nfriotadxy 5476 |
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