Theorem snssd

Description: The singleton of an element of a class is a subset of the class (deduction form). (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

	Ref	Expression
Hypothesis	snssd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝐵 )
Assertion	snssd	⊢ ( 𝜑 → { 𝐴 } ⊆ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		snssd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝐵 )
2		snssi	⊢ ( 𝐴 ∈ 𝐵 → { 𝐴 } ⊆ 𝐵 )
3	1 2	syl	⊢ ( 𝜑 → { 𝐴 } ⊆ 𝐵 )