Theorem pnfnre2 11375

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 11374	. 2 ⊢ +∞ ∉ ℝ
2	1	neli 3067	1 ⊢ ¬ +∞ ∈ ℝ

This proof depends on syntax axioms:  ¬ wn 3   ∈ wcel 2147  ℝcr 11223  +∞cpnf 11364

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735  ax-sep 5252  ax-resscn 11281

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-nel 3066  df-rab 3417  df-v 3456  df-ss 3901  df-in 4094  df-pw 4562  df-uni 4871  df-pnf 11369

This theorem is used by:  nn0xmulclb  33430