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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 2166 | . 2 | |
2 | nfv 1521 | . . 3 | |
3 | nfcvd 2313 | . . . . 5 | |
4 | nfeqd.1 | . . . . 5 | |
5 | 3, 4 | nfeqd 2327 | . . . 4 |
6 | nfeqd.2 | . . . . 5 | |
7 | 6 | nfcrd 2326 | . . . 4 |
8 | 5, 7 | nfand 1561 | . . 3 |
9 | 2, 8 | nfexd 1754 | . 2 |
10 | 1, 9 | nfxfrd 1468 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wnf 1453 wex 1485 wcel 2141 wnfc 2299 |
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 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-4 1503 ax-17 1519 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-cleq 2163 df-clel 2166 df-nfc 2301 |
This theorem is referenced by: nfneld 2443 nfraldw 2502 nfraldxy 2503 nfrexdxy 2504 nfreudxy 2643 nfsbc1d 2971 nfsbcd 2974 sbcrext 3032 nfsbcdw 3083 nfbrd 4034 nfriotadxy 5817 nfixpxy 6695 |
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