Theorem renepnfd

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

	Ref	Expression
Hypothesis	rexrd.1	$$⊢\phi \to A\in ℝ$$
Assertion	renepnfd	$$⊢\phi \to A\ne \mathrm{+\infty }$$

Proof

Step	Hyp	Ref	Expression
1		rexrd.1	$$⊢\phi \to A\in ℝ$$
2		renepnf	$$⊢A\in ℝ\to A\ne \mathrm{+\infty }$$
3	1 2	syl	$$⊢\phi \to A\ne \mathrm{+\infty }$$