Theorem eldisjssd

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

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

Proof

Step	Hyp	Ref	Expression
1		eldisjssd.1	⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )
2		eldisjss	⊢ ( 𝐴 ⊆ 𝐵 → ( ElDisj 𝐵 → ElDisj 𝐴 ) )
3	1 2	syl	⊢ ( 𝜑 → ( ElDisj 𝐵 → ElDisj 𝐴 ) )