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Metamath Proof Explorer

Theorem unissi

Description: Subclass relationship for subclass union. Inference form of uniss . (Contributed by David Moews, 1-May-2017)

Ref Expression
Hypothesis unissi.1 ⊢ 𝐴 ⊆ 𝐵
Assertion unissi ∪ 𝐴 ⊆ ∪ 𝐵

Proof

Step Hyp Ref Expression
1 unissi.1 ⊢ 𝐴 ⊆ 𝐵
2 uniss ⊢ ( 𝐴 ⊆ 𝐵 → ∪ 𝐴 ⊆ ∪ 𝐵 )
3 1 2 ax-mp ⊢ ∪ 𝐴 ⊆ ∪ 𝐵