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Theorem dfnfc2 4237
 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 2581 . . . 4
2 id 22 . . . 4
31, 2nfeqd 2587 . . 3
43alrimiv 1767 . 2
5 simpr 462 . . . . . 6
6 df-nfc 2568 . . . . . . 7
7 elsn 4012 . . . . . . . . 9
87nfbii 1689 . . . . . . . 8
98albii 1685 . . . . . . 7
106, 9bitri 252 . . . . . 6
115, 10sylibr 215 . . . . 5
1211nfunid 4226 . . . 4
13 nfa1 1956 . . . . . 6
14 nfnf1 1958 . . . . . . 7
1514nfal 2007 . . . . . 6
1613, 15nfan 1988 . . . . 5
17 unisng 4235 . . . . . . 7
1817sps 1920 . . . . . 6
1918adantr 466 . . . . 5
2016, 19nfceqdf 2575 . . . 4
2112, 20mpbid 213 . . 3
2221ex 435 . 2
234, 22impbid2 207 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370  wal 1435   wceq 1437  wnf 1661   wcel 1872  wnfc 2566  csn 3998  cuni 4219 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ral 2776  df-rex 2777  df-v 3082  df-un 3441  df-sn 3999  df-pr 4001  df-uni 4220 This theorem is referenced by:  eusv2nf  4622
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