Theorem pnfnre2 11178

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 11177	. 2 ⊢ +∞ ∉ ℝ
2	1	neli 3040	1 ⊢ ¬ +∞ ∈ ℝ

Syntax hints:  ¬ wn 3   ∈ wcel 2119  ℝcr 11028  +∞cpnf 11167

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711  ax-sep 5218  ax-pr 5362  ax-un 7678  ax-resscn 11086

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-3an 1094  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-nel 3039  df-rab 3392  df-v 3433  df-un 3888  df-in 3890  df-ss 3900  df-pw 4531  df-sn 4556  df-pr 4558  df-uni 4839  df-pnf 11172

This theorem is referenced by:  nn0xmulclb  32863