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Mirrors > Home > ILE Home > Th. List > nfel | Unicode version |
Description: Hypothesis builder for elementhood. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfnfc.1 | |
nfeq.2 |
Ref | Expression |
---|---|
nfel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-clel 2077 | . 2 | |
2 | nfcv 2219 | . . . . 5 | |
3 | nfnfc.1 | . . . . 5 | |
4 | 2, 3 | nfeq 2226 | . . . 4 |
5 | nfeq.2 | . . . . 5 | |
6 | 5 | nfcri 2213 | . . . 4 |
7 | 4, 6 | nfan 1497 | . . 3 |
8 | 7 | nfex 1568 | . 2 |
9 | 1, 8 | nfxfr 1403 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 102 wceq 1284 wnf 1389 wex 1421 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-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-cleq 2074 df-clel 2077 df-nfc 2208 |
This theorem is referenced by: nfel1 2229 nfel2 2231 nfnel 2346 elabgf 2736 elrabf 2747 sbcel12g 2921 nfdisjv 3778 rabxfrd 4219 ffnfvf 5345 elabgft1 10588 elabgf2 10590 bj-rspgt 10596 |
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