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	⊢ ( 𝜑 → 𝐴 ∈ 𝐶 )
	prssd.2	⊢ ( 𝜑 → 𝐵 ∈ 𝐶 )
Assertion	prssd	⊢ ( 𝜑 → { 𝐴 , 𝐵 } ⊆ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		prssd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝐶 )
2		prssd.2	⊢ ( 𝜑 → 𝐵 ∈ 𝐶 )
3		prssi	⊢ ( ( 𝐴 ∈ 𝐶 ∧ 𝐵 ∈ 𝐶 ) → { 𝐴 , 𝐵 } ⊆ 𝐶 )
4	1 2 3	syl2anc	⊢ ( 𝜑 → { 𝐴 , 𝐵 } ⊆ 𝐶 )