Theorem pnfnre2 11310

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 11309	. 2 ⊢ +∞ ∉ ℝ
2	1	neli 3048	1 ⊢ ¬ +∞ ∈ ℝ

Syntax hints:  ¬ wn 3   ∈ wcel 2108  ℝcr 11161  +∞cpnf 11299

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-sep 5305  ax-pr 5441  ax-un 7761  ax-resscn 11219

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1542  df-ex 1779  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-nel 3047  df-rab 3437  df-v 3483  df-un 3971  df-in 3973  df-ss 3983  df-pw 4610  df-sn 4635  df-pr 4637  df-uni 4916  df-pnf 11304

This theorem is referenced by:  nn0xmulclb  32796