Metamath Proof Explorer


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 ≠ +∞ )