Theorem heeq1

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

	Ref	Expression
Assertion	heeq1	⊢ ( 𝑅 = 𝑆 → ( 𝑅 hereditary 𝐴 ↔ 𝑆 hereditary 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ 𝐴 = 𝐴
2		heeq12	⊢ ( ( 𝑅 = 𝑆 ∧ 𝐴 = 𝐴 ) → ( 𝑅 hereditary 𝐴 ↔ 𝑆 hereditary 𝐴 ) )
3	1 2	mpan2	⊢ ( 𝑅 = 𝑆 → ( 𝑅 hereditary 𝐴 ↔ 𝑆 hereditary 𝐴 ) )