Theorem pnfnre2 11351

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 11350	. 2 ⊢ +∞ ∉ ℝ
2	1	neli 3063	1 ⊢ ¬ +∞ ∈ ℝ

This proof depends on syntax axioms:  ¬ wn 3   ∈ wcel 2144  ℝcr 11199  +∞cpnf 11340

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732  ax-sep 5248  ax-resscn 11257

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-nel 3062  df-rab 3413  df-v 3452  df-ss 3896  df-in 4091  df-pw 4558  df-uni 4867  df-pnf 11345

This theorem is used by:  nn0xmulclb  33363