Theorem nn0nepnfd

Description: No standard nonnegative integer equals positive infinity, deduction form. (Contributed by AV, 10-Dec-2020)

	Ref	Expression
Hypothesis	nn0xnn0d.1	$$⊢\phi \to A\in {\mathbb{N}}_0$$
Assertion	nn0nepnfd	$$⊢\phi \to A\ne \mathrm{+\infty }$$

Proof

Step	Hyp	Ref	Expression
1		nn0xnn0d.1	$$⊢\phi \to A\in {\mathbb{N}}_0$$
2		nn0nepnf	$$⊢A\in {\mathbb{N}}_0\to A\ne \mathrm{+\infty }$$
3	1 2	syl	$$⊢\phi \to A\ne \mathrm{+\infty }$$