Theorem sseld

Description: Membership deduction from subclass relationship. (Contributed by NM, 15-Nov-1995)

	Ref	Expression
Hypothesis	sseld.1	⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )
Assertion	sseld	⊢ ( 𝜑 → ( 𝐶 ∈ 𝐴 → 𝐶 ∈ 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		sseld.1	⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )
2		ssel	⊢ ( 𝐴 ⊆ 𝐵 → ( 𝐶 ∈ 𝐴 → 𝐶 ∈ 𝐵 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐶 ∈ 𝐴 → 𝐶 ∈ 𝐵 ) )