Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > intid | Unicode version |
Description: The intersection of all sets to which a set belongs is the singleton of that set. (Contributed by NM, 5-Jun-2009.) |
Ref | Expression |
---|---|
intid.1 |
Ref | Expression |
---|---|
intid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | intid.1 | . . . 4 | |
2 | 1 | snex 4109 | . . 3 |
3 | eleq2 2203 | . . . 4 | |
4 | 1 | snid 3556 | . . . 4 |
5 | 3, 4 | intmin3 3798 | . . 3 |
6 | 2, 5 | ax-mp 5 | . 2 |
7 | 1 | elintab 3782 | . . . 4 |
8 | id 19 | . . . 4 | |
9 | 7, 8 | mpgbir 1429 | . . 3 |
10 | snssi 3664 | . . 3 | |
11 | 9, 10 | ax-mp 5 | . 2 |
12 | 6, 11 | eqssi 3113 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 cab 2125 cvv 2686 wss 3071 csn 3527 cint 3771 |
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-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 |
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-v 2688 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-int 3772 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |