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Mirrors > Home > NFE Home > Th. List > ncfinex | Unicode version |
Description: The finite cardinality of a set exists. (Contributed by SF, 27-Jan-2015.) |
Ref | Expression |
---|---|
ncfinex | Ncfin |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ncfin 4442 | . 2 Ncfin Nn | |
2 | iotaex 4356 | . 2 Nn | |
3 | 1, 2 | eqeltri 2423 | 1 Ncfin |
Colors of variables: wff setvar class |
Syntax hints: wa 358 wcel 1710 cvv 2859 cio 4337 Nn cnnc 4373 Ncfin cncfin 4434 |
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 ax-nin 4078 |
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-eu 2208 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-ral 2619 df-rex 2620 df-v 2861 df-sbc 3047 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-ss 3259 df-nul 3551 df-sn 3741 df-pr 3742 df-uni 3892 df-iota 4339 df-ncfin 4442 |
This theorem is referenced by: ncvspfin 4538 vfintle 4546 vfin1cltv 4547 vfinncvntsp 4549 vfinspss 4551 vfinspclt 4552 vfinspeqtncv 4553 vfinncsp 4554 |
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