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Theorem dfnfc2 4033
 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:   ,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem dfnfc2
StepHypRef Expression
1 nfcvd 2573 . . . 4
2 id 20 . . . 4
31, 2nfeqd 2586 . . 3
43alrimiv 1641 . 2
5 simpr 448 . . . . . 6
6 df-nfc 2561 . . . . . . 7
7 elsn 3829 . . . . . . . . 9
87nfbii 1578 . . . . . . . 8
98albii 1575 . . . . . . 7
106, 9bitri 241 . . . . . 6
115, 10sylibr 204 . . . . 5
1211nfunid 4022 . . . 4
13 nfa1 1806 . . . . . 6
14 nfnf1 1808 . . . . . . 7
1514nfal 1864 . . . . . 6
1613, 15nfan 1846 . . . . 5
17 unisng 4032 . . . . . . 7
1817sps 1770 . . . . . 6
1918adantr 452 . . . . 5
2016, 19nfceqdf 2571 . . . 4
2112, 20mpbid 202 . . 3
2221ex 424 . 2
234, 22impbid2 196 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wnf 1553   wceq 1652   wcel 1725  wnfc 2559  csn 3814  cuni 4015 This theorem is referenced by:  eusv2nf  4721 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-v 2958  df-un 3325  df-sn 3820  df-pr 3821  df-uni 4016
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