Theorem prnz

Description: A pair containing a set is not empty. (Contributed by NM, 9-Apr-1994)

	Ref	Expression
Hypothesis	prnz.1	⊢ 𝐴 ∈ V
Assertion	prnz	⊢ { 𝐴 , 𝐵 } ≠ ∅

Proof

Step	Hyp	Ref	Expression
1		prnz.1	⊢ 𝐴 ∈ V
2	1	prid1	⊢ 𝐴 ∈ { 𝐴 , 𝐵 }
3	2	ne0ii	⊢ { 𝐴 , 𝐵 } ≠ ∅