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Theorem mnfnepnf 11318
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 11317 . 2 +∞ ≠ -∞
21necomi 2994 1 -∞ ≠ +∞
Colors of variables: wff setvar class
Syntax hints:  wne 2939  +∞cpnf 11293  -∞cmnf 11294
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707  ax-sep 5295  ax-pow 5364  ax-un 7756  ax-cnex 11212
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-ne 2940  df-rab 3436  df-v 3481  df-un 3955  df-in 3957  df-ss 3967  df-pw 4601  df-sn 4626  df-pr 4628  df-uni 4907  df-pnf 11298  df-mnf 11299  df-xr 11300
This theorem is referenced by:  xrnepnf  13161  xnegmnf  13253  xaddmnf1  13271  xaddmnf2  13272  mnfaddpnf  13274  xaddnepnf  13280  xmullem2  13308  xadddilem  13337  resup  13908
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