Theorem pnfnre2 11257

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 11256	. 2 ⊢ +∞ ∉ ℝ
2	1	neli 3042	1 ⊢ ¬ +∞ ∈ ℝ

Syntax hints:  ¬ wn 3   ∈ wcel 2098  ℝcr 11108  +∞cpnf 11246

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 2697  ax-sep 5292  ax-pr 5420  ax-un 7721  ax-resscn 11166

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-nel 3041  df-rab 3427  df-v 3470  df-un 3948  df-in 3950  df-ss 3960  df-pw 4599  df-sn 4624  df-pr 4626  df-uni 4903  df-pnf 11251

This theorem is referenced by:  nn0xmulclb  32489