Theorem pnfnre2 11174

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 11173	. 2 ⊢ +∞ ∉ ℝ
2	1	neli 3038	1 ⊢ ¬ +∞ ∈ ℝ

Syntax hints:  ¬ wn 3   ∈ wcel 2113  ℝcr 11025  +∞cpnf 11163

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2708  ax-sep 5241  ax-pr 5377  ax-un 7680  ax-resscn 11083

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-nel 3037  df-rab 3400  df-v 3442  df-un 3906  df-in 3908  df-ss 3918  df-pw 4556  df-sn 4581  df-pr 4583  df-uni 4864  df-pnf 11168

This theorem is referenced by:  nn0xmulclb  32851