Theorem pnfnre2 11251

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 11250	. 2 ⊢ +∞ ∉ ℝ
2	1	neli 3072	1 ⊢ ¬ +∞ ∈ ℝ

Syntax hints:  ¬ wn 3   ∈ wcel 2149  ℝcr 11099  +∞cpnf 11240

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741  ax-sep 5261  ax-resscn 11157

This theorem depends on definitions:  df-bi 210  df-an 401  df-3an 1103  df-tru 1570  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-nel 3071  df-rab 3424  df-v 3465  df-in 3920  df-ss 3930  df-pw 4569  df-uni 4877  df-pnf 11245

This theorem is referenced by:  nn0xmulclb  33057