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Mirrors > Home > MPE Home > Th. List > Mathboxes > onsuccon | Structured version Unicode version |
Description: A successor ordinal number is a connected topology. (Contributed by Chen-Pang He, 16-Oct-2015.) |
Ref | Expression |
---|---|
onsuccon |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | suceq 4887 |
. . 3
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2 | 1 | eleq1d 2521 |
. 2
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3 | 0elon 4875 |
. . . 4
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4 | 3 | elimel 3955 |
. . 3
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5 | 4 | onsucconi 28422 |
. 2
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6 | 2, 5 | dedth 3944 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1954 ax-ext 2431 ax-sep 4516 ax-nul 4524 ax-pow 4573 ax-pr 4634 ax-un 6477 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3or 966 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2265 df-mo 2266 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2602 df-ne 2647 df-ral 2801 df-rex 2802 df-rab 2805 df-v 3074 df-sbc 3289 df-dif 3434 df-un 3436 df-in 3438 df-ss 3445 df-pss 3447 df-nul 3741 df-if 3895 df-pw 3965 df-sn 3981 df-pr 3983 df-tp 3985 df-op 3987 df-uni 4195 df-br 4396 df-opab 4454 df-mpt 4455 df-tr 4489 df-eprel 4735 df-id 4739 df-po 4744 df-so 4745 df-fr 4782 df-we 4784 df-ord 4825 df-on 4826 df-suc 4828 df-xp 4949 df-rel 4950 df-cnv 4951 df-co 4952 df-dm 4953 df-iota 5484 df-fun 5523 df-fn 5524 df-fv 5529 df-topgen 14496 df-top 18630 df-bases 18632 df-cld 18750 df-con 19143 |
This theorem is referenced by: ordtopcon 28424 |
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