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Metamath Proof Explorer

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	$⊢ φ \to A \in B$
	Assertion	snssd	$⊢ φ \to \{A\} \subseteq B$

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