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Mirrors > Home > ILE Home > Th. List > xrex | Unicode version |
Description: The set of extended reals exists. (Contributed by NM, 24-Dec-2006.) |
Ref | Expression |
---|---|
xrex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xr 7722 |
. 2
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2 | reex 7672 |
. . 3
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3 | pnfxr 7736 |
. . . 4
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4 | mnfxr 7740 |
. . . 4
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5 | prexg 4091 |
. . . 4
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6 | 3, 4, 5 | mp2an 420 |
. . 3
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7 | 2, 6 | unex 4320 |
. 2
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8 | 1, 7 | eqeltri 2185 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-13 1472 ax-14 1473 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-sep 4004 ax-pow 4056 ax-pr 4089 ax-un 4313 ax-cnex 7630 ax-resscn 7631 |
This theorem depends on definitions: df-bi 116 df-tru 1315 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-rex 2394 df-v 2657 df-un 3039 df-in 3041 df-ss 3048 df-pw 3476 df-sn 3497 df-pr 3498 df-uni 3701 df-pnf 7720 df-mnf 7721 df-xr 7722 |
This theorem is referenced by: ixxval 9566 ixxf 9568 ixxex 9569 ispsmet 12306 isxmet 12328 xmetunirn 12341 blfvalps 12368 blex 12370 |
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