Theorem nn0nepnfd

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

	Ref	Expression
Hypothesis	nn0xnn0d.1	⊢ ( 𝜑 → 𝐴 ∈ ℕ0 )
Assertion	nn0nepnfd	⊢ ( 𝜑 → 𝐴 ≠ +∞ )

Proof

Step	Hyp	Ref	Expression
1		nn0xnn0d.1	⊢ ( 𝜑 → 𝐴 ∈ ℕ0 )
2		nn0nepnf	⊢ ( 𝐴 ∈ ℕ0 → 𝐴 ≠ +∞ )
3	1 2	syl	⊢ ( 𝜑 → 𝐴 ≠ +∞ )