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Mirrors > Home > MPE Home > Th. List > xrex | Structured version Visualization version Unicode version |
Description: The set of extended reals exists. (Contributed by NM, 24-Dec-2006.) |
Ref | Expression |
---|---|
xrex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xr 10078 | . 2 | |
2 | reex 10027 | . . 3 | |
3 | prex 4909 | . . 3 | |
4 | 2, 3 | unex 6956 | . 2 |
5 | 1, 4 | eqeltri 2697 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wcel 1990 cvv 3200 cun 3572 cpr 4179 cr 9935 cpnf 10071 cmnf 10072 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-nul 4789 ax-pr 4906 ax-un 6949 ax-cnex 9992 ax-resscn 9993 |
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-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-sn 4178 df-pr 4180 df-uni 4437 df-xr 10078 |
This theorem is referenced by: ixxval 12183 ixxf 12185 ixxex 12186 limsuple 14209 limsuplt 14210 limsupbnd1 14213 prdsds 16124 letsr 17227 xrsbas 19762 xrsadd 19763 xrsmul 19764 xrsle 19766 xrs1mnd 19784 xrs10 19785 xrs1cmn 19786 xrge0subm 19787 xrge0cmn 19788 xrsds 19789 znle 19884 leordtval2 21016 lecldbas 21023 ispsmet 22109 isxmet 22129 imasdsf1olem 22178 blfvalps 22188 nmoffn 22515 nmofval 22518 xrsxmet 22612 xrge0gsumle 22636 xrge0tsms 22637 xrlimcnp 24695 xrge00 29686 xrge0tsmsd 29785 xrhval 30062 icof 39411 elicores 39760 fuzxrpmcn 40054 gsumge0cl 40588 ovnval2b 40766 volicorescl 40767 ovnsubaddlem1 40784 |
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