Theorem ssun

Description: A condition that implies inclusion in the union of two classes. (Contributed by NM, 23-Nov-2003)

	Ref	Expression
Assertion	ssun	⊢ ( ( 𝐴 ⊆ 𝐵 ∨ 𝐴 ⊆ 𝐶 ) → 𝐴 ⊆ ( 𝐵 ∪ 𝐶 ) )

Proof

Step	Hyp	Ref	Expression
1		ssun3	⊢ ( 𝐴 ⊆ 𝐵 → 𝐴 ⊆ ( 𝐵 ∪ 𝐶 ) )
2		ssun4	⊢ ( 𝐴 ⊆ 𝐶 → 𝐴 ⊆ ( 𝐵 ∪ 𝐶 ) )
3	1 2	jaoi	⊢ ( ( 𝐴 ⊆ 𝐵 ∨ 𝐴 ⊆ 𝐶 ) → 𝐴 ⊆ ( 𝐵 ∪ 𝐶 ) )