Description: Coelements on A is a relation. (Contributed by Peter Mazsa, 5-Oct-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | relcoels | ⊢ Rel ∼ 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relcoss | ⊢ Rel ≀ ( ◡ E ↾ 𝐴 ) | |
2 | df-coels | ⊢ ∼ 𝐴 = ≀ ( ◡ E ↾ 𝐴 ) | |
3 | 2 | releqi | ⊢ ( Rel ∼ 𝐴 ↔ Rel ≀ ( ◡ E ↾ 𝐴 ) ) |
4 | 1 3 | mpbir | ⊢ Rel ∼ 𝐴 |