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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 2153 | . 2 | |
2 | nfv 1508 | . . 3 | |
3 | nfcvd 2300 | . . . . 5 | |
4 | nfeqd.1 | . . . . 5 | |
5 | 3, 4 | nfeqd 2314 | . . . 4 |
6 | nfeqd.2 | . . . . 5 | |
7 | 6 | nfcrd 2313 | . . . 4 |
8 | 5, 7 | nfand 1548 | . . 3 |
9 | 2, 8 | nfexd 1741 | . 2 |
10 | 1, 9 | nfxfrd 1455 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wnf 1440 wex 1472 wcel 2128 wnfc 2286 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-4 1490 ax-17 1506 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-cleq 2150 df-clel 2153 df-nfc 2288 |
This theorem is referenced by: nfneld 2430 nfraldw 2489 nfraldxy 2490 nfrexdxy 2491 nfreudxy 2630 nfsbc1d 2953 nfsbcd 2956 sbcrext 3014 nfsbcdw 3065 nfbrd 4009 nfriotadxy 5788 nfixpxy 6662 |
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