Theorem disjimi

Description: Every disjoint relation generates equivalent cosets by the relation, inference version. (Contributed by Peter Mazsa, 30-Sep-2021)

	Ref	Expression
Hypothesis	disjimi.1	⊢ Disj 𝑅
Assertion	disjimi	⊢ EqvRel ≀ 𝑅

Proof

Step	Hyp	Ref	Expression
1		disjimi.1	⊢ Disj 𝑅
2		disjim	⊢ ( Disj 𝑅 → EqvRel ≀ 𝑅 )
3	1 2	ax-mp	⊢ EqvRel ≀ 𝑅