![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > mnfnepnf | Structured version Visualization version GIF version |
Description: Minus and plus infinity are different. (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
mnfnepnf | ⊢ -∞ ≠ +∞ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pnfnemnf 11210 | . 2 ⊢ +∞ ≠ -∞ | |
2 | 1 | necomi 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 |