Theorem eldisjssi

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

	Ref	Expression
Hypothesis	eldisjssi.1	⊢ 𝐴 ⊆ 𝐵
Assertion	eldisjssi	⊢ ( ElDisj 𝐵 → ElDisj 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		eldisjssi.1	⊢ 𝐴 ⊆ 𝐵
2		eldisjss	⊢ ( 𝐴 ⊆ 𝐵 → ( ElDisj 𝐵 → ElDisj 𝐴 ) )
3	1 2	ax-mp	⊢ ( ElDisj 𝐵 → ElDisj 𝐴 )