Theorem sselda

Description: Membership deduction from subclass relationship. (Contributed by NM, 26-Jun-2014)

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

Proof

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