Theorem disjeqi

Description: Equality theorem for disjoints, inference version. (Contributed by Peter Mazsa, 22-Sep-2021)

	Ref	Expression
Hypothesis	disjeqi.1	⊢ 𝐴 = 𝐵
Assertion	disjeqi	⊢ ( Disj 𝐴 ↔ Disj 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		disjeqi.1	⊢ 𝐴 = 𝐵
2		disjeq	⊢ ( 𝐴 = 𝐵 → ( Disj 𝐴 ↔ Disj 𝐵 ) )
3	1 2	ax-mp	⊢ ( Disj 𝐴 ↔ Disj 𝐵 )