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Mirrors > Home > ILE Home > Th. List > neleq2 | Unicode version |
Description: Equality theorem for negated membership. (Contributed by NM, 20-Nov-1994.) |
Ref | Expression |
---|---|
neleq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq2 2181 | . . 3 | |
2 | 1 | notbid 641 | . 2 |
3 | df-nel 2381 | . 2 | |
4 | df-nel 2381 | . 2 | |
5 | 2, 3, 4 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wceq 1316 wcel 1465 wnel 2380 |
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-in1 588 ax-in2 589 ax-5 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-17 1491 ax-ial 1499 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-cleq 2110 df-clel 2113 df-nel 2381 |
This theorem is referenced by: neleq12d 2386 |
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