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Theorem mnfnepnf 10690
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 10689 . 2 +∞ ≠ -∞
21necomi 3044 1 -∞ ≠ +∞
Colors of variables: wff setvar class
Syntax hints:  wne 2990  +∞cpnf 10665  -∞cmnf 10666
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 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2159  ax-12 2176  ax-ext 2773  ax-sep 5170  ax-pow 5234  ax-un 7445  ax-cnex 10586
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-nfc 2941  df-ne 2991  df-rab 3118  df-v 3446  df-un 3889  df-in 3891  df-ss 3901  df-pw 4502  df-sn 4529  df-pr 4531  df-uni 4804  df-pnf 10670  df-mnf 10671  df-xr 10672
This theorem is referenced by:  xrnepnf  12505  xnegmnf  12595  xaddmnf1  12613  xaddmnf2  12614  mnfaddpnf  12616  xaddnepnf  12622  xmullem2  12650  xadddilem  12679  resup  13234
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