Theorem pnfnre2 11300

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 11299	. 2 ⊢ +∞ ∉ ℝ
2	1	neli 3063	1 ⊢ ¬ +∞ ∈ ℝ

This proof depends on syntax axioms:  ¬ wn 3   ∈ wcel 2145  ℝcr 11148  +∞cpnf 11289

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 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732  ax-sep 5251  ax-resscn 11206

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-nel 3062  df-rab 3413  df-v 3452  df-in 3906  df-ss 3916  df-pw 4559  df-uni 4868  df-pnf 11294

This theorem is used by:  nn0xmulclb  33274