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Mirrors > Home > ILE Home > Th. List > tpnz | Unicode version |
Description: A triplet containing a set is not empty. (Contributed by NM, 10-Apr-1994.) |
Ref | Expression |
---|---|
tpnz.1 |
Ref | Expression |
---|---|
tpnz |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tpnz.1 | . . 3 | |
2 | 1 | tpid1 3481 | . 2 |
3 | ne0i 3230 | . 2 | |
4 | 2, 3 | ax-mp 7 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1393 wne 2204 cvv 2557 c0 3224 ctp 3377 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3or 886 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ne 2206 df-v 2559 df-dif 2920 df-un 2922 df-nul 3225 df-sn 3381 df-pr 3382 df-tp 3383 |
This theorem is referenced by: (None) |
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