Theorem bnj1293

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

	Ref	Expression
Hypothesis	bnj1293.1	⊢ 𝐴 = ( 𝐵 ∩ 𝐶 )
Assertion	bnj1293	⊢ 𝐴 ⊆ 𝐶

Proof

Step	Hyp	Ref	Expression
1		bnj1293.1	⊢ 𝐴 = ( 𝐵 ∩ 𝐶 )
2		inss2	⊢ ( 𝐵 ∩ 𝐶 ) ⊆ 𝐶
3	1 2	eqsstri	⊢ 𝐴 ⊆ 𝐶