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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
StepHypRef Expression
1 nfcvd 2620 . . . 4
2 id 22 . . . 4
31, 2nfeqd 2626 . . 3
43alrimiv 1719 . 2
5 simpr 461 . . . . . 6
6 df-nfc 2607 . . . . . . 7
7 elsn 4043 . . . . . . . . 9
87nfbii 1644 . . . . . . . 8
98albii 1640 . . . . . . 7
106, 9bitri 249 . . . . . 6
115, 10sylibr 212 . . . . 5
1211nfunid 4256 . . . 4
13 nfa1 1897 . . . . . 6
14 nfnf1 1899 . . . . . . 7
1514nfal 1947 . . . . . 6
1613, 15nfan 1928 . . . . 5
17 unisng 4265 . . . . . . 7
1817sps 1865 . . . . . 6
1918adantr 465 . . . . 5
2016, 19nfceqdf 2614 . . . 4
2112, 20mpbid 210 . . 3
2221ex 434 . 2
234, 22impbid2 204 1
 Colors of variables: wff setvar class 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
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