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Metamath Proof Explorer

Theorem bnj1292

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

Ref Expression
Hypothesis bnj1292.1 ⊢ 𝐴 = ( 𝐵 ∩ 𝐶 )
Assertion bnj1292 𝐴 ⊆ 𝐵

Proof

Step Hyp Ref Expression
1 bnj1292.1 ⊢ 𝐴 = ( 𝐵 ∩ 𝐶 )
2 inss1 ⊢ ( 𝐵 ∩ 𝐶 ) ⊆ 𝐵
3 1 2 eqsstri ⊢ 𝐴 ⊆ 𝐵