Theorem disjeqd

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

	Ref	Expression
Hypothesis	disjeqd.1	$$⊢\phi \to A=B$$
Assertion	disjeqd	$$⊢\phi \to \left(DisjA\leftrightarrow DisjB\right)$$

Proof

Step	Hyp	Ref	Expression
1		disjeqd.1	$$⊢\phi \to A=B$$
2		disjeq	$$⊢A=B\to \left(DisjA\leftrightarrow DisjB\right)$$
3	1 2	syl	$$⊢\phi \to \left(DisjA\leftrightarrow DisjB\right)$$