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Theorem pnfnre2 40516
 Description: Plus infinity is not a real number. (Contributed by Glauco Siliprandi, 23-Oct-2021.)
Assertion
Ref Expression
pnfnre2 ¬ +∞ ∈ ℝ

Proof of Theorem pnfnre2
StepHypRef Expression
1 pnfnre 10418 . 2 +∞ ∉ ℝ
21neli 3076 1 ¬ +∞ ∈ ℝ
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ∈ wcel 2106  ℝcr 10271  +∞cpnf 10408 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2054  ax-8 2108  ax-9 2115  ax-10 2134  ax-11 2149  ax-12 2162  ax-13 2333  ax-ext 2753  ax-sep 5017  ax-nul 5025  ax-pr 5138  ax-un 7226  ax-resscn 10329 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-3an 1073  df-tru 1605  df-ex 1824  df-nf 1828  df-sb 2012  df-clab 2763  df-cleq 2769  df-clel 2773  df-nfc 2920  df-nel 3075  df-rex 3095  df-rab 3098  df-v 3399  df-dif 3794  df-un 3796  df-in 3798  df-ss 3805  df-nul 4141  df-pw 4380  df-sn 4398  df-pr 4400  df-uni 4672  df-pnf 10413 This theorem is referenced by: (None)
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