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Mirrors > Home > ILE Home > Th. List > a16nf | Unicode version |
Description: If there is only one element in the universe, then everything satisfies . (Contributed by Mario Carneiro, 7-Oct-2016.) |
Ref | Expression |
---|---|
a16nf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfae 1697 | . 2 | |
2 | a16g 1836 | . 2 | |
3 | 1, 2 | nfd 1503 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1329 wnf 1436 |
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-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 |
This theorem is referenced by: nfsbxy 1913 nfsbxyt 1914 dvelimor 1991 |
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