Theorem disjeq1d

Description: Equality theorem for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016)

	Ref	Expression
Hypothesis	disjeq1d.1	|- ( ph -> A = B )
Assertion	disjeq1d	|- ( ph -> ( Disj_ x e. A C <-> Disj_ x e. B C ) )

Proof

Step	Hyp	Ref	Expression
1		disjeq1d.1	|- ( ph -> A = B )
2		disjeq1	|- ( A = B -> ( Disj_ x e. A C <-> Disj_ x e. B C ) )
3	1 2	syl	|- ( ph -> ( Disj_ x e. A C <-> Disj_ x e. B C ) )