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 ∈ 𝐶 ∧ 𝐵 ∈ 𝐶 ) → { 𝐴 , 𝐵 } ⊆ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		prssg	⊢ ( ( 𝐴 ∈ 𝐶 ∧ 𝐵 ∈ 𝐶 ) → ( ( 𝐴 ∈ 𝐶 ∧ 𝐵 ∈ 𝐶 ) ↔ { 𝐴 , 𝐵 } ⊆ 𝐶 ) )
2	1	ibi	⊢ ( ( 𝐴 ∈ 𝐶 ∧ 𝐵 ∈ 𝐶 ) → { 𝐴 , 𝐵 } ⊆ 𝐶 )