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Metamath Proof Explorer

Theorem eqvrel1cossxrnidres

Description: The cosets by a range Cartesian product with a restricted identity relation are in equivalence relation. (Contributed by Peter Mazsa, 31-Dec-2021)

		Ref	Expression
	Assertion	eqvrel1cossxrnidres	⊢ EqvRel ≀ ( 𝑅 ⋉ ( I ↾ 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		disjALTVxrnidres	⊢ Disj ( 𝑅 ⋉ ( I ↾ 𝐴 ) )
2	1	disjimi	⊢ EqvRel ≀ ( 𝑅 ⋉ ( I ↾ 𝐴 ) )