Theorem mnfnepnf 11441

Description: Minus and plus infinity are different (common case). (Contributed by David A. Wheeler, 8-Dec-2018.)

Assertion

Ref	Expression
mnfnepnf	|- -oo =/= +oo

Proof of Theorem mnfnepnf

Step	Hyp	Ref	Expression
1		pnfnemnf 11440	. 2 |- +oo =/= -oo
2	1	necomi 2697	1 |- -oo =/= +oo

Syntax hints:   =/= wne 2641   +oocpnf 9690   -oocmnf 9691

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-8 1906  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-pow 4579  ax-un 6602  ax-cnex 9613

This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-nel 2644  df-rex 2762  df-rab 2765  df-v 3033  df-un 3395  df-in 3397  df-ss 3404  df-pw 3944  df-sn 3960  df-pr 3962  df-uni 4191  df-pnf 9695  df-mnf 9696  df-xr 9697

This theorem is referenced by:  xrnepnf  11443  xnegmnf  11526  xaddmnf1  11544  xaddmnf2  11545  mnfaddpnf  11547  xaddnepnf  11552  xmullem2  11576  xadddilem  11605  resup  12127