Theorem disjssi

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

	Ref	Expression
Hypothesis	disjssi.1	⊢ 𝐴 ⊆ 𝐵
Assertion	disjssi	⊢ ( Disj 𝐵 → Disj 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		disjssi.1	⊢ 𝐴 ⊆ 𝐵
2		disjss	⊢ ( 𝐴 ⊆ 𝐵 → ( Disj 𝐵 → Disj 𝐴 ) )
3	1 2	ax-mp	⊢ ( Disj 𝐵 → Disj 𝐴 )