Theorem prssd

Description: Deduction version of prssi : A pair of elements of a class is a subset of the class. (Contributed by Glauco Siliprandi, 17-Aug-2020)

	Ref	Expression
Hypotheses	prssd.1	|- ( ph -> A e. C )
	prssd.2	|- ( ph -> B e. C )
Assertion	prssd	|- ( ph -> { A , B } C_ C )

Proof

Step	Hyp	Ref	Expression
1		prssd.1	|- ( ph -> A e. C )
2		prssd.2	|- ( ph -> B e. C )
3		prssi	|- ( ( A e. C /\ B e. C ) -> { A , B } C_ C )
4	1 2 3	syl2anc	|- ( ph -> { A , B } C_ C )