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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 2166 | . 2 | |
2 | nfcv 2312 | . . . . 5 | |
3 | nfnfc.1 | . . . . 5 | |
4 | 2, 3 | nfeq 2320 | . . . 4 |
5 | nfeq.2 | . . . . 5 | |
6 | 5 | nfcri 2306 | . . . 4 |
7 | 4, 6 | nfan 1558 | . . 3 |
8 | 7 | nfex 1630 | . 2 |
9 | 1, 8 | nfxfr 1467 | 1 |
Colors of variables: wff set class |
Syntax hints: 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-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-cleq 2163 df-clel 2166 df-nfc 2301 |
This theorem is referenced by: nfel1 2323 nfel2 2325 nfnel 2442 elabgf 2872 elrabf 2884 sbcel12g 3064 nfdisjv 3978 rabxfrd 4454 ffnfvf 5655 mptelixpg 6712 elabgft1 13813 elabgf2 13815 bj-rspgt 13821 |
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