Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > 2pwuninelg | Unicode version |
Description: The power set of the power set of the union of a set does not belong to the set. This theorem provides a way of constructing a new set that doesn't belong to a given set. (Contributed by Jim Kingdon, 14-Jan-2020.) |
Ref | Expression |
---|---|
2pwuninelg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | en2lp 4297 | . 2 | |
2 | pwuni 3963 | . . . 4 | |
3 | elpwg 3390 | . . . 4 | |
4 | 2, 3 | mpbiri 166 | . . 3 |
5 | ax-ia3 106 | . . 3 | |
6 | 4, 5 | syl 14 | . 2 |
7 | 1, 6 | mtoi 622 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 102 wcel 1433 wss 2973 cpw 3382 cuni 3601 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-setind 4280 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-v 2603 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-uni 3602 |
This theorem is referenced by: mnfnre 7161 |
Copyright terms: Public domain | W3C validator |