Theorem heeq2

Description: Equality law for relations being herditary over a class. (Contributed by RP, 27-Mar-2020)

	Ref	Expression
Assertion	heeq2	⊢ ( 𝐴 = 𝐵 → ( 𝑅 hereditary 𝐴 ↔ 𝑅 hereditary 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ 𝑅 = 𝑅
2		heeq12	⊢ ( ( 𝑅 = 𝑅 ∧ 𝐴 = 𝐵 ) → ( 𝑅 hereditary 𝐴 ↔ 𝑅 hereditary 𝐵 ) )
3	1 2	mpan	⊢ ( 𝐴 = 𝐵 → ( 𝑅 hereditary 𝐴 ↔ 𝑅 hereditary 𝐵 ) )