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Theorem mnfnepnf 10296
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 10295 . 2 +∞ ≠ -∞
21necomi 2996 1 -∞ ≠ +∞
Colors of variables: wff setvar class
Syntax hints:  wne 2942  +∞cpnf 10272  -∞cmnf 10273
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-8 2146  ax-9 2153  ax-10 2173  ax-11 2189  ax-12 2202  ax-13 2407  ax-ext 2750  ax-sep 4912  ax-pow 4971  ax-un 7095  ax-cnex 10193
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2049  df-clab 2757  df-cleq 2763  df-clel 2766  df-nfc 2901  df-ne 2943  df-nel 3046  df-rex 3066  df-rab 3069  df-v 3351  df-un 3726  df-in 3728  df-ss 3735  df-pw 4297  df-sn 4315  df-pr 4317  df-uni 4573  df-pnf 10277  df-mnf 10278  df-xr 10279
This theorem is referenced by:  xrnepnf  12156  xnegmnf  12245  xaddmnf1  12263  xaddmnf2  12264  mnfaddpnf  12266  xaddnepnf  12272  xmullem2  12299  xadddilem  12328  resup  12873
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