Theorem elun1

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

	Ref	Expression
Assertion	elun1	⊢ ( 𝐴 ∈ 𝐵 → 𝐴 ∈ ( 𝐵 ∪ 𝐶 ) )

Proof

Step	Hyp	Ref	Expression
1		ssun1	⊢ 𝐵 ⊆ ( 𝐵 ∪ 𝐶 )
2	1	sseli	⊢ ( 𝐴 ∈ 𝐵 → 𝐴 ∈ ( 𝐵 ∪ 𝐶 ) )