MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  mnfnepnf Structured version   Visualization version   GIF version

Theorem mnfnepnf 11211
Description: Minus and plus infinity are different. (Contributed by David A. Wheeler, 8-Dec-2018.)
Assertion
Ref Expression
mnfnepnf -∞ ≠ +∞

Proof of Theorem mnfnepnf
StepHypRef Expression
1 pnfnemnf 11210 . 2 +∞ ≠ -∞
21necomi 2998 1 -∞ ≠ +∞
Colors of variables: wff setvar class
Syntax hints:  wne 2943  +∞cpnf 11186  -∞cmnf 11187
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707  ax-sep 5256  ax-pow 5320  ax-un 7672  ax-cnex 11107
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-ne 2944  df-rab 3408  df-v 3447  df-un 3915  df-in 3917  df-ss 3927  df-pw 4562  df-sn 4587  df-pr 4589  df-uni 4866  df-pnf 11191  df-mnf 11192  df-xr 11193
This theorem is referenced by:  xrnepnf  13039  xnegmnf  13129  xaddmnf1  13147  xaddmnf2  13148  mnfaddpnf  13150  xaddnepnf  13156  xmullem2  13184  xadddilem  13213  resup  13772
  Copyright terms: Public domain W3C validator