Description: An equivalence relation is a relation. (Contributed by Peter Mazsa, 2-Jun-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | eqvrelrel | ⊢ ( EqvRel 𝑅 → Rel 𝑅 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfeqvrel2 | ⊢ ( EqvRel 𝑅 ↔ ( ( ( I ↾ dom 𝑅 ) ⊆ 𝑅 ∧ ◡ 𝑅 ⊆ 𝑅 ∧ ( 𝑅 ∘ 𝑅 ) ⊆ 𝑅 ) ∧ Rel 𝑅 ) ) | |
2 | 1 | simprbi | ⊢ ( EqvRel 𝑅 → Rel 𝑅 ) |