Theorem pnfnre2 11285

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 11284	. 2 ⊢ +∞ ∉ ℝ
2	1	neli 3037	1 ⊢ ¬ +∞ ∈ ℝ

Syntax hints:  ¬ wn 3   ∈ wcel 2107  ℝcr 11136  +∞cpnf 11274

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2706  ax-sep 5276  ax-pr 5412  ax-un 7737  ax-resscn 11194

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-clel 2808  df-nel 3036  df-rab 3420  df-v 3465  df-un 3936  df-in 3938  df-ss 3948  df-pw 4582  df-sn 4607  df-pr 4609  df-uni 4888  df-pnf 11279

This theorem is referenced by:  nn0xmulclb  32712