New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > elfin | Unicode version |
Description: Membership in the set of finite sets. (Contributed by SF, 19-Jan-2015.) |
Ref | Expression |
---|---|
elfin | Fin Nn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fin 4380 | . . 3 Fin Nn | |
2 | 1 | eleq2i 2417 | . 2 Fin Nn |
3 | eluni2 3895 | . 2 Nn Nn | |
4 | 2, 3 | bitri 240 | 1 Fin Nn |
Colors of variables: wff setvar class |
Syntax hints: wb 176 wcel 1710 wrex 2615 cuni 3891 Nn cnnc 4373 Fin cfin 4376 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-rex 2620 df-v 2861 df-uni 3892 df-fin 4380 |
This theorem is referenced by: 0fin 4423 snfi 4431 ssfin 4470 vfinnc 4471 sfinltfin 4535 ncssfin 6151 pw1fin 6169 nntccl 6170 finnc 6242 ncfin 6246 |
Copyright terms: Public domain | W3C validator |