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Mirrors > Home > MPE Home > Th. List > eltop2 | Structured version Visualization version Unicode version |
Description: Membership in a topology. (Contributed by NM, 19-Jul-2006.) |
Ref | Expression |
---|---|
eltop2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tgtop 19989 |
. . 3
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2 | 1 | eleq2d 2514 |
. 2
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3 | eltg2b 19974 |
. 2
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4 | 2, 3 | bitr3d 259 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-8 1889 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-sep 4525 ax-nul 4534 ax-pow 4581 ax-pr 4639 ax-un 6583 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-ral 2742 df-rex 2743 df-rab 2746 df-v 3047 df-sbc 3268 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-pw 3953 df-sn 3969 df-pr 3971 df-op 3975 df-uni 4199 df-br 4403 df-opab 4462 df-mpt 4463 df-id 4749 df-xp 4840 df-rel 4841 df-cnv 4842 df-co 4843 df-dm 4844 df-iota 5546 df-fun 5584 df-fv 5590 df-topgen 15342 df-top 19921 |
This theorem is referenced by: isclo 20103 cncnp 20296 ist1-2 20363 hauscmp 20422 llycmpkgen2 20565 ptpjopn 20627 txkgen 20667 xkococn 20675 xkoinjcn 20702 fclscf 21040 subgntr 21121 opnsubg 21122 qustgpopn 21134 prdsxmslem2 21544 zdis 21834 efopn 23603 cvmopnlem 30001 neibastop3 31018 |
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