Theorem mzpcln0

Description: Corrolary of mzpclall : polynomially closed function sets are not empty. (Contributed by Stefan O'Rear, 4-Oct-2014)

	Ref	Expression
Assertion	mzpcln0	$$⊢V\in \mathrm{V}\to \mathrm{mzPolyCld}\left(V\right)\ne \varnothing$$

Proof

Step	Hyp	Ref	Expression
1		mzpclall	$$⊢V\in \mathrm{V}\to {\mathbb{Z}}^{\left({\mathbb{Z}}^V\right)}\in \mathrm{mzPolyCld}\left(V\right)$$
2	1	ne0d	$$⊢V\in \mathrm{V}\to \mathrm{mzPolyCld}\left(V\right)\ne \varnothing$$