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	$$⊢\phi \to A\in B$$
Assertion	snssd	$$⊢\phi \to \left\{A\right\}\subseteq B$$

Proof

Step	Hyp	Ref	Expression
1		snssd.1	$$⊢\phi \to A\in B$$
2		snssi	$$⊢A\in B\to \left\{A\right\}\subseteq B$$
3	1 2	syl	$$⊢\phi \to \left\{A\right\}\subseteq B$$