Theorem ssun3

Description: Subclass law for union of classes. (Contributed by NM, 5-Aug-1993)

	Ref	Expression
Assertion	ssun3	⊢ ( 𝐴 ⊆ 𝐵 → 𝐴 ⊆ ( 𝐵 ∪ 𝐶 ) )

Proof

Step	Hyp	Ref	Expression
1		ssun1	⊢ 𝐵 ⊆ ( 𝐵 ∪ 𝐶 )
2		sstr2	⊢ ( 𝐴 ⊆ 𝐵 → ( 𝐵 ⊆ ( 𝐵 ∪ 𝐶 ) → 𝐴 ⊆ ( 𝐵 ∪ 𝐶 ) ) )
3	1 2	mpi	⊢ ( 𝐴 ⊆ 𝐵 → 𝐴 ⊆ ( 𝐵 ∪ 𝐶 ) )