Theorem pnfnre2 40126

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 10273	. 2 ⊢ +∞ ∉ ℝ
2	1	neli 3037	1 ⊢ ¬ +∞ ∈ ℝ

Syntax hints:  ¬ wn 3   ∈ wcel 2139  ℝcr 10127  +∞cpnf 10263

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-8 2141  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740  ax-sep 4933  ax-nul 4941  ax-pr 5055  ax-un 7114  ax-resscn 10185

This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-nel 3036  df-rex 3056  df-rab 3059  df-v 3342  df-dif 3718  df-un 3720  df-in 3722  df-ss 3729  df-nul 4059  df-pw 4304  df-sn 4322  df-pr 4324  df-uni 4589  df-pnf 10268

This theorem is referenced by: (None)