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 3039	1 ⊢ ¬ +∞ ∈ ℝ

Syntax hints:  ¬ wn 3   ∈ wcel 2114  ℝcr 11029  +∞cpnf 11167

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-sep 5242  ax-pr 5378  ax-un 7682  ax-resscn 11087

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-nel 3038  df-rab 3401  df-v 3443  df-un 3907  df-in 3909  df-ss 3919  df-pw 4557  df-sn 4582  df-pr 4584  df-uni 4865  df-pnf 11172

This theorem is referenced by:  nn0xmulclb  32832