New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > n0 | Unicode version |
Description: A nonempty class has at least one element. Proposition 5.17(1) of [TakeutiZaring] p. 20. (Contributed by NM, 29-Sep-2006.) |
Ref | Expression |
---|---|
n0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2489 | . 2 | |
2 | 1 | n0f 3558 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 176 wex 1541 wcel 1710 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: neq0 3560 reximdva0 3561 n0moeu 3562 pssnel 3615 r19.2z 3639 r19.2zb 3640 r19.3rz 3641 r19.3rzv 3643 uniintsn 3963 iunn0 4026 pw10b 4166 ndisjrelk 4323 prepeano4 4451 nnpw1ex 4484 tfindi 4496 tfinsuc 4498 sfinltfin 4535 vfintle 4546 nulnnn 4556 opabn0 4716 dmxp 4923 xpnz 5045 dmsnn0 5064 ecdmn0 5967 mapsspm 6021 mapsspw 6022 map0 6025 ncssfin 6151 ncspw1eu 6159 nntccl 6170 ce0nnul 6177 ce0nnulb 6182 fce 6188 lecidg 6196 lec0cg 6198 lecncvg 6199 addlec 6208 nc0le1 6216 |
Copyright terms: Public domain | W3C validator |