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Theorem finex 4397

Description: The class of all finite sets is a set. (Contributed by SF, 19-Jan-2015.)

**Assertion**
Ref	Expression
finex	⊢ Fin ∈ V

**Proof of Theorem finex**
Step	Hyp	Ref	Expression
1		df-fin 4380	. 2 ⊢ Fin = ∪ Nn
2		nncex 4396	. . 3 ⊢ Nn ∈ V
3	2	uniex 4317	. 2 ⊢ ∪ Nn ∈ V
4	1, 3	eqeltri 2423	1 ⊢ Fin ∈ V

Colors of variables: wff setvar class

Syntax hints: ∈ wcel 1710 Vcvv 2859 ∪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 ax-nin 4078 ax-xp 4079 ax-cnv 4080 ax-1c 4081 ax-sset 4082 ax-si 4083 ax-ins2 4084 ax-ins3 4085 ax-typlower 4086 ax-sn 4087

This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 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-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-symdif 3216 df-ss 3259 df-nul 3551 df-if 3663 df-pw 3724 df-sn 3741 df-pr 3742 df-uni 3892 df-int 3927 df-opk 4058 df-1c 4136 df-pw1 4137 df-uni1 4138 df-xpk 4185 df-cnvk 4186 df-ins2k 4187 df-ins3k 4188 df-imak 4189 df-cok 4190 df-p6 4191 df-sik 4192 df-ssetk 4193 df-imagek 4194 df-addc 4378 df-nnc 4379 df-fin 4380

This theorem is referenced by: ssfin 4470 nchoicelem11 6299 nchoicelem18 6306