Theorem ssun4

Description: Subclass law for union of classes. (Contributed by NM, 14-Aug-1994)

	Ref	Expression
Assertion	ssun4	⊢ ( 𝐴 ⊆ 𝐵 → 𝐴 ⊆ ( 𝐶 ∪ 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		ssun2	⊢ 𝐵 ⊆ ( 𝐶 ∪ 𝐵 )
2		sstr2	⊢ ( 𝐴 ⊆ 𝐵 → ( 𝐵 ⊆ ( 𝐶 ∪ 𝐵 ) → 𝐴 ⊆ ( 𝐶 ∪ 𝐵 ) ) )
3	1 2	mpi	⊢ ( 𝐴 ⊆ 𝐵 → 𝐴 ⊆ ( 𝐶 ∪ 𝐵 ) )