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Metamath Proof Explorer

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 ) )