Theorem unissi

Description: Subclass relationship for subclass union. Inference form of uniss . (Contributed by David Moews, 1-May-2017)

	Ref	Expression
Hypothesis	unissi.1	⊢ 𝐴 ⊆ 𝐵
Assertion	unissi	⊢ ∪ 𝐴 ⊆ ∪ 𝐵

Proof

Step	Hyp	Ref	Expression
1		unissi.1	⊢ 𝐴 ⊆ 𝐵
2		uniss	⊢ ( 𝐴 ⊆ 𝐵 → ∪ 𝐴 ⊆ ∪ 𝐵 )
3	1 2	ax-mp	⊢ ∪ 𝐴 ⊆ ∪ 𝐵