Theorem ssd

Description: A sufficient condition for a subclass relationship. (Contributed by Glauco Siliprandi, 3-Jan-2021)

	Ref	Expression
Hypothesis	ssd.1	⊢ ( ( 𝜑 ∧ 𝑥 ∈ 𝐴 ) → 𝑥 ∈ 𝐵 )
Assertion	ssd	⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		ssd.1	⊢ ( ( 𝜑 ∧ 𝑥 ∈ 𝐴 ) → 𝑥 ∈ 𝐵 )
2		nfv	⊢ Ⅎ 𝑥 𝜑
3	2 1	ssdf	⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )