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Mirrors > Home > NFE Home > Th. List > n0f | Unicode version |
Description: A nonempty class has at least one element. Proposition 5.17(1) of [TakeutiZaring] p. 20. This version of n0 3559 requires only that not be free in, rather than not occur in, . (Contributed by NM, 17-Oct-2003.) |
Ref | Expression |
---|---|
n0f.1 |
Ref | Expression |
---|---|
n0f |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | n0f.1 | . . . . 5 | |
2 | nfcv 2489 | . . . . 5 | |
3 | 1, 2 | cleqf 2513 | . . . 4 |
4 | noel 3554 | . . . . . 6 | |
5 | 4 | nbn 336 | . . . . 5 |
6 | 5 | albii 1566 | . . . 4 |
7 | 3, 6 | bitr4i 243 | . . 3 |
8 | 7 | necon3abii 2546 | . 2 |
9 | df-ex 1542 | . 2 | |
10 | 8, 9 | bitr4i 243 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wb 176 wal 1540 wex 1541 wceq 1642 wcel 1710 wnfc 2476 wne 2516 c0 3550 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-dif 3215 df-nul 3551 |
This theorem is referenced by: n0 3559 abn0 3568 |
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