Theorem inss1

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	inss1	⊢ ( 𝐴 ∩ 𝐵 ) ⊆ 𝐴

Proof

Step	Hyp	Ref	Expression
1		elinel1	⊢ ( 𝑥 ∈ ( 𝐴 ∩ 𝐵 ) → 𝑥 ∈ 𝐴 )
2	1	ssriv	⊢ ( 𝐴 ∩ 𝐵 ) ⊆ 𝐴