Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2153 | . 2 | |
2 | nfcv 2299 | . . . . 5 | |
3 | nfnfc.1 | . . . . 5 | |
4 | 2, 3 | nfeq 2307 | . . . 4 |
5 | nfeq.2 | . . . . 5 | |
6 | 5 | nfcri 2293 | . . . 4 |
7 | 4, 6 | nfan 1545 | . . 3 |
8 | 7 | nfex 1617 | . 2 |
9 | 1, 8 | nfxfr 1454 | 1 |
Colors of variables: wff set class |
Syntax hints: 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-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-cleq 2150 df-clel 2153 df-nfc 2288 |
This theorem is referenced by: nfel1 2310 nfel2 2312 nfnel 2429 elabgf 2854 elrabf 2866 sbcel12g 3046 nfdisjv 3955 rabxfrd 4430 ffnfvf 5627 mptelixpg 6680 elabgft1 13394 elabgf2 13396 bj-rspgt 13402 |
Copyright terms: Public domain | W3C validator |