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Theorem pnfnre2 11292
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 11291 . 2 +∞ ∉ ℝ
21neli 3044 1 ¬ +∞ ∈ ℝ
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wcel 2098  cr 11143  +∞cpnf 11281
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2698  ax-sep 5301  ax-pr 5431  ax-un 7744  ax-resscn 11201
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2705  df-cleq 2719  df-clel 2805  df-nel 3043  df-rab 3429  df-v 3473  df-un 3952  df-in 3954  df-ss 3964  df-pw 4606  df-sn 4631  df-pr 4633  df-uni 4911  df-pnf 11286
This theorem is referenced by:  nn0xmulclb  32559
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