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Metamath Proof Explorer

Theorem bnj931

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Hypothesis bnj931.1 ⊢ 𝐴 = ( 𝐵 ∪ 𝐶 )
Assertion bnj931 𝐵 ⊆ 𝐴

Proof

Step Hyp Ref Expression
1 bnj931.1 ⊢ 𝐴 = ( 𝐵 ∪ 𝐶 )
2 ssun1 ⊢ 𝐵 ⊆ ( 𝐵 ∪ 𝐶 )
3 2 1 sseqtrri ⊢ 𝐵 ⊆ 𝐴