Theorem renepnfd

Description: No (finite) real equals plus infinity. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypothesis	rexrd.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
Assertion	renepnfd	⊢ ( 𝜑 → 𝐴 ≠ +∞ )

Proof

Step	Hyp	Ref	Expression
1		rexrd.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		renepnf	⊢ ( 𝐴 ∈ ℝ → 𝐴 ≠ +∞ )
3	1 2	syl	⊢ ( 𝜑 → 𝐴 ≠ +∞ )