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	$$⊢\phi \to A\in C$$
	prssd.2	$$⊢\phi \to B\in C$$
Assertion	prssd	$$⊢\phi \to \left\{A,B\right\}\subseteq C$$

Proof

Step	Hyp	Ref	Expression
1		prssd.1	$$⊢\phi \to A\in C$$
2		prssd.2	$$⊢\phi \to B\in C$$
3		prssi	$$⊢\left(A\in C\wedge B\in C\right)\to \left\{A,B\right\}\subseteq C$$
4	1 2 3	syl2anc	$$⊢\phi \to \left\{A,B\right\}\subseteq C$$