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