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Metamath Proof Explorer

Theorem inss2

Description: The intersection of two classes is a subset of one of them. Part of Exercise 12 of TakeutiZaring p. 18. (Contributed by NM, 27-Apr-1994)

		Ref	Expression
	Assertion	inss2	⊢ ( 𝐴 ∩ 𝐵 ) ⊆ 𝐵

Proof

Step	Hyp	Ref	Expression
1		incom	⊢ ( 𝐵 ∩ 𝐴 ) = ( 𝐴 ∩ 𝐵 )
2		inss1	⊢ ( 𝐵 ∩ 𝐴 ) ⊆ 𝐵
3	1 2	eqsstrri	⊢ ( 𝐴 ∩ 𝐵 ) ⊆ 𝐵