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Mirrors > Home > ILE Home > Th. List > isbasis3g | Unicode version |
Description: Express the predicate "the set is a basis for a topology". Definition of basis in [Munkres] p. 78. (Contributed by NM, 17-Jul-2006.) |
Ref | Expression |
---|---|
isbasis3g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isbasis2g 12201 | . 2 | |
2 | elssuni 3759 | . . . . . 6 | |
3 | 2 | rgen 2483 | . . . . 5 |
4 | eluni2 3735 | . . . . . . 7 | |
5 | 4 | biimpi 119 | . . . . . 6 |
6 | 5 | rgen 2483 | . . . . 5 |
7 | 3, 6 | pm3.2i 270 | . . . 4 |
8 | 7 | biantrur 301 | . . 3 |
9 | df-3an 964 | . . 3 | |
10 | 8, 9 | bitr4i 186 | . 2 |
11 | 1, 10 | syl6bb 195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 962 wcel 1480 wral 2414 wrex 2415 cin 3065 wss 3066 cuni 3731 ctb 12198 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-in 3072 df-ss 3079 df-pw 3507 df-uni 3732 df-bases 12199 |
This theorem is referenced by: (None) |
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