This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem prssi

Description: A pair of elements of a class is a subset of the class. (Contributed by NM, 16-Jan-2015)

		Ref	Expression
	Assertion	prssi	$⊢ (A \in C \land B \in C) \to \{A, B\} \subseteq C$

Step	Hyp	Ref	Expression
1		prssg	$⊢ (A \in C \land B \in C) \to ((A \in C \land B \in C) \leftrightarrow \{A, B\} \subseteq C)$
2	1	ibi	$⊢ (A \in C \land B \in C) \to \{A, B\} \subseteq C$