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Mirrors > Home > ILE Home > Th. List > 0nep0 | Unicode version |
Description: The empty set and its power set are not equal. (Contributed by NM, 23-Dec-1993.) |
Ref | Expression |
---|---|
0nep0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0ex 4108 | . . 3 | |
2 | 1 | snnz 3694 | . 2 |
3 | 2 | necomi 2420 | 1 |
Colors of variables: wff set class |
Syntax hints: wne 2335 c0 3408 csn 3575 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-ext 2147 ax-nul 4107 |
This theorem depends on definitions: df-bi 116 df-tru 1346 df-nf 1449 df-sb 1751 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2296 df-ne 2336 df-v 2727 df-dif 3117 df-nul 3409 df-sn 3581 |
This theorem is referenced by: 0inp0 4144 opthprc 4654 2dom 6767 exmidpw 6870 exmidaclem 7160 pw1dom2 7179 |
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