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Mirrors > Home > ILE Home > Th. List > rex0 | Unicode version |
Description: Vacuous existential quantification is false. (Contributed by NM, 15-Oct-2003.) |
Ref | Expression |
---|---|
rex0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3255 | . . 3 | |
2 | 1 | pm2.21i 607 | . 2 |
3 | 2 | nrex 2453 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wcel 1433 wrex 2349 c0 3251 |
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 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-dif 2975 df-nul 3252 |
This theorem is referenced by: 0iun 3735 exfzdc 9249 |
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