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Mirrors > Home > MPE Home > Th. List > pnfex | Structured version Visualization version Unicode version |
Description: Plus infinity exists (common case). (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
pnfex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pnfxr 10092 | . 2 | |
2 | 1 | elexi 3213 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wcel 1990 cvv 3200 cpnf 10071 cxr 10073 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-pow 4843 ax-un 6949 ax-cnex 9992 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rex 2918 df-v 3202 df-un 3579 df-in 3581 df-ss 3588 df-pw 4160 df-sn 4178 df-pr 4180 df-uni 4437 df-pnf 10076 df-xr 10078 |
This theorem is referenced by: mnfxr 10096 elxnn0 11365 elxr 11950 xnegex 12039 xaddval 12054 xmulval 12056 xrinfmss 12140 hashgval 13120 hashinf 13122 hashfxnn0 13124 hashfOLD 13126 pcval 15549 pc0 15559 ramcl2 15720 iccpnfhmeo 22744 taylfval 24113 xrlimcnp 24695 xrge0iifcv 29980 xrge0iifiso 29981 xrge0iifhom 29983 sge0f1o 40599 sge0sup 40608 sge0pnfmpt 40662 |
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