Theorem pnfnre2 11224

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 11223	. 2 ⊢ +∞ ∉ ℝ
2	1	neli 3063	1 ⊢ ¬ +∞ ∈ ℝ

Syntax hints:  ¬ wn 3   ∈ wcel 2142  ℝcr 11072  +∞cpnf 11213

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829  ax-5 1930  ax-6 1987  ax-7 2028  ax-8 2144  ax-9 2152  ax-ext 2734  ax-sep 5246  ax-resscn 11130

This theorem depends on definitions:  df-bi 209  df-an 400  df-3an 1100  df-tru 1563  df-ex 1800  df-sb 2091  df-clab 2741  df-cleq 2754  df-clel 2837  df-nel 3062  df-rab 3415  df-v 3456  df-in 3911  df-ss 3921  df-pw 4557  df-uni 4866  df-pnf 11218

This theorem is referenced by:  nn0xmulclb  32973