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Metamath Proof Explorer

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 } ≠ ∅