Theorem eldisjeqi

Description: Equality theorem for disjoint elementhood, inference version. (Contributed by Peter Mazsa, 23-Sep-2021)

	Ref	Expression
Hypothesis	eldisjeqi.1	⊢ 𝐴 = 𝐵
Assertion	eldisjeqi	⊢ ( ElDisj 𝐴 ↔ ElDisj 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		eldisjeqi.1	⊢ 𝐴 = 𝐵
2		eldisjeq	⊢ ( 𝐴 = 𝐵 → ( ElDisj 𝐴 ↔ ElDisj 𝐵 ) )
3	1 2	ax-mp	⊢ ( ElDisj 𝐴 ↔ ElDisj 𝐵 )