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Mirrors > Home > ILE Home > Th. List > isbasisg | Unicode version |
Description: Express the predicate "the set is a basis for a topology". (Contributed by NM, 17-Jul-2006.) |
Ref | Expression |
---|---|
isbasisg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ineq1 3270 | . . . . . 6 | |
2 | 1 | unieqd 3747 | . . . . 5 |
3 | 2 | sseq2d 3127 | . . . 4 |
4 | 3 | raleqbi1dv 2634 | . . 3 |
5 | 4 | raleqbi1dv 2634 | . 2 |
6 | df-bases 12213 | . 2 | |
7 | 5, 6 | elab2g 2831 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1331 wcel 1480 wral 2416 cin 3070 wss 3071 cpw 3510 cuni 3736 ctb 12212 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-in 3077 df-ss 3084 df-uni 3737 df-bases 12213 |
This theorem is referenced by: isbasis2g 12215 basis1 12217 baspartn 12220 |
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