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Mirrors > Home > MPE Home > Th. List > letopuni | Structured version Visualization version GIF version |
Description: The topology of the extended reals. (Contributed by Mario Carneiro, 3-Sep-2015.) |
Ref | Expression |
---|---|
letopuni | ⊢ ℝ* = ∪ (ordTop‘ ≤ ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | letopon 22701 | . 2 ⊢ (ordTop‘ ≤ ) ∈ (TopOn‘ℝ*) | |
2 | 1 | toponunii 22410 | 1 ⊢ ℝ* = ∪ (ordTop‘ ≤ ) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 ∪ cuni 4908 ‘cfv 6541 ℝ*cxr 11244 ≤ cle 11246 ordTopcordt 17442 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 ax-sep 5299 ax-nul 5306 ax-pow 5363 ax-pr 5427 ax-un 7722 ax-cnex 11163 ax-resscn 11164 ax-pre-lttri 11181 ax-pre-lttrn 11182 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3or 1089 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ne 2942 df-nel 3048 df-ral 3063 df-rex 3072 df-reu 3378 df-rab 3434 df-v 3477 df-sbc 3778 df-csb 3894 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-pss 3967 df-nul 4323 df-if 4529 df-pw 4604 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-int 4951 df-br 5149 df-opab 5211 df-mpt 5232 df-tr 5266 df-id 5574 df-eprel 5580 df-po 5588 df-so 5589 df-fr 5631 df-we 5633 df-xp 5682 df-rel 5683 df-cnv 5684 df-co 5685 df-dm 5686 df-rn 5687 df-res 5688 df-ima 5689 df-ord 6365 df-on 6366 df-lim 6367 df-suc 6368 df-iota 6493 df-fun 6543 df-fn 6544 df-f 6545 df-f1 6546 df-fo 6547 df-f1o 6548 df-fv 6549 df-om 7853 df-1o 8463 df-er 8700 df-en 8937 df-dom 8938 df-sdom 8939 df-fin 8940 df-fi 9403 df-pnf 11247 df-mnf 11248 df-xr 11249 df-ltxr 11250 df-le 11251 df-topgen 17386 df-ordt 17444 df-ps 18516 df-tsr 18517 df-top 22388 df-topon 22405 df-bases 22441 |
This theorem is referenced by: lecldbas 22715 xrsmopn 24320 xrge0mulc1cn 32910 icccldii 47505 |
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