Theorem pnfnre2 11157

Description: Plus infinity is not a real number. (Contributed by Glauco Siliprandi, 23-Oct-2021.)

Assertion

Ref	Expression
pnfnre2	⊢ ¬ +∞ ∈ ℝ

Proof of Theorem pnfnre2

Step	Hyp	Ref	Expression
1		pnfnre 11156	. 2 ⊢ +∞ ∉ ℝ
2	1	neli 3031	1 ⊢ ¬ +∞ ∈ ℝ

Syntax hints:  ¬ wn 3   ∈ wcel 2109  ℝcr 11008  +∞cpnf 11146

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701  ax-sep 5235  ax-pr 5371  ax-un 7671  ax-resscn 11066

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-nel 3030  df-rab 3395  df-v 3438  df-un 3908  df-in 3910  df-ss 3920  df-pw 4553  df-sn 4578  df-pr 4580  df-uni 4859  df-pnf 11151

This theorem is referenced by:  nn0xmulclb  32715