Theorem dfnfc2 4267

Description: An alternative statement of the effective freeness of a class , when it is a set. (Contributed by Mario Carneiro, 14-Oct-2016.)

Assertion

Ref	Expression
dfnfc2

Distinct variable groups:   ,   ,

Proof of Theorem dfnfc2

Step	Hyp	Ref	Expression
1		nfcvd 2620	. . . 4
2		id 22	. . . 4
3	1, 2	nfeqd 2626	. . 3
4	3	alrimiv 1719	. 2
5		simpr 461	. . . . . 6
6		df-nfc 2607	. . . . . . 7
7		elsn 4043	. . . . . . . . 9
8	7	nfbii 1644	. . . . . . . 8
9	8	albii 1640	. . . . . . 7
10	6, 9	bitri 249	. . . . . 6
11	5, 10	sylibr 212	. . . . 5
12	11	nfunid 4256	. . . 4
13		nfa1 1897	. . . . . 6
14		nfnf1 1899	. . . . . . 7
15	14	nfal 1947	. . . . . 6
16	13, 15	nfan 1928	. . . . 5
17		unisng 4265	. . . . . . 7
18	17	sps 1865	. . . . . 6
19	18	adantr 465	. . . . 5
20	16, 19	nfceqdf 2614	. . . 4
21	12, 20	mpbid 210	. . 3
22	21	ex 434	. 2
23	4, 22	impbid2 204	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  F/wnf 1616  e.wcel 1818  F/_wnfc 2605  {csn 4029  U.cuni 4249

This theorem is referenced by:  eusv2nf  4650

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111  df-un 3480  df-sn 4030  df-pr 4032  df-uni 4250