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	$$⊢⟨“A”⟩\ne \varnothing$$

Proof

Step	Hyp	Ref	Expression
1		df-s1	$$⊢⟨“A”⟩=\left\{⟨0,\mathrm{I}\left(A\right)⟩\right\}$$
2		opex	$$⊢⟨0,\mathrm{I}\left(A\right)⟩\in \mathrm{V}$$
3	2	snnz	$$⊢\left\{⟨0,\mathrm{I}\left(A\right)⟩\right\}\ne \varnothing$$
4	1 3	eqnetri	$$⊢⟨“A”⟩\ne \varnothing$$