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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 7516 |
. 2
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2 | reex 7466 |
. . 3
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3 | pnfxr 7530 |
. . . 4
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4 | mnfxr 7534 |
. . . 4
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5 | prexg 4036 |
. . . 4
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6 | 3, 4, 5 | mp2an 417 |
. . 3
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7 | 2, 6 | unex 4264 |
. 2
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8 | 1, 7 | eqeltri 2160 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-13 1449 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3955 ax-pow 4007 ax-pr 4034 ax-un 4258 ax-cnex 7426 ax-resscn 7427 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-rex 2365 df-v 2621 df-un 3003 df-in 3005 df-ss 3012 df-pw 3429 df-sn 3450 df-pr 3451 df-uni 3652 df-pnf 7514 df-mnf 7515 df-xr 7516 |
This theorem is referenced by: ixxval 9304 ixxf 9306 ixxex 9307 |
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