Theorem s1nz

Description: A singleton word is not the empty string. (Contributed by Mario Carneiro, 27-Feb-2016) (Proof shortened by Kyle Wyonch, 18-Jul-2021)

	Ref	Expression
Assertion	s1nz	⊢ ⟨“ 𝐴 ”⟩ ≠ ∅

Proof

Step	Hyp	Ref	Expression
1		df-s1	⊢ ⟨“ 𝐴 ”⟩ = { ⟨ 0 , ( I ‘ 𝐴 ) ⟩ }
2		opex	⊢ ⟨ 0 , ( I ‘ 𝐴 ) ⟩ ∈ V
3	2	snnz	⊢ { ⟨ 0 , ( I ‘ 𝐴 ) ⟩ } ≠ ∅
4	1 3	eqnetri	⊢ ⟨“ 𝐴 ”⟩ ≠ ∅