Theorem pnfnre2 39628

Description: Plus infinity is not a real number. (Contributed by Glauco Siliprandi, 23-Oct-2021.)

Assertion

Ref	Expression
pnfnre2	|- -. +oo e. RR

Proof of Theorem pnfnre2

Step	Hyp	Ref	Expression
1		pnfnre 10081	. 2 |- +oo e/ RR
2	1	neli 2899	1 |- -. +oo e. RR

Syntax hints:   -. wn 3   e. wcel 1990   RRcr 9935   +oocpnf 10071

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-8 1992  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-sep 4781  ax-nul 4789  ax-pr 4906  ax-un 6949  ax-resscn 9993

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1039  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-nel 2898  df-rex 2918  df-rab 2921  df-v 3202  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-pw 4160  df-sn 4178  df-pr 4180  df-uni 4437  df-pnf 10076

This theorem is referenced by: (None)