Theorem eldisjssd

Description: Subclass theorem for disjoint elementhood, deduction version. (Contributed by Peter Mazsa, 28-Sep-2021)

	Ref	Expression
Hypothesis	eldisjssd.1	|- ( ph -> A C_ B )
Assertion	eldisjssd	|- ( ph -> ( ElDisj B -> ElDisj A ) )

Proof

Step	Hyp	Ref	Expression
1		eldisjssd.1	|- ( ph -> A C_ B )
2		eldisjss	|- ( A C_ B -> ( ElDisj B -> ElDisj A ) )
3	1 2	syl	|- ( ph -> ( ElDisj B -> ElDisj A ) )