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Metamath Proof Explorer

Theorem elun2

Description: Membership law for union of classes. (Contributed by NM, 30-Aug-1993)

Ref Expression
Assertion elun2 ( 𝐴 ∈ 𝐵 → 𝐴 ∈ ( 𝐶 ∪ 𝐵 ) )

Proof

Step Hyp Ref Expression
1 ssun2 ⊢ 𝐵 ⊆ ( 𝐶 ∪ 𝐵 )
2 1 sseli ⊢ ( 𝐴 ∈ 𝐵 → 𝐴 ∈ ( 𝐶 ∪ 𝐵 ) )