Description: The membership relation and the identity relation are disjoint. Variable-free version of nelaneq . (Proposed by BJ, 18-Jun-2022.) (Contributed by AV, 18-Jun-2022)
Ref | Expression | ||
---|---|---|---|
Assertion | epinid0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eprel | ||
2 | df-id | ||
3 | 1 2 | ineq12i | |
4 | inopab | ||
5 | nelaneq | ||
6 | 5 | gen2 | |
7 | opab0 | ||
8 | 6 7 | mpbir | |
9 | 3 4 8 | 3eqtri |