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Theorem dfnfc2 3909
 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 2490 . . . 4
2 id 19 . . . 4
31, 2nfeqd 2503 . . 3
43alrimiv 1631 . 2
5 simpr 447 . . . . . 6
6 df-nfc 2478 . . . . . . 7
7 elsn 3748 . . . . . . . . 9
87nfbii 1569 . . . . . . . 8
98albii 1566 . . . . . . 7
106, 9bitri 240 . . . . . 6
115, 10sylibr 203 . . . . 5
1211nfunid 3898 . . . 4
13 nfa1 1788 . . . . . 6
14 nfnf1 1790 . . . . . . 7
1514nfal 1842 . . . . . 6
1613, 15nfan 1824 . . . . 5
17 unisng 3908 . . . . . . 7
1817sps 1754 . . . . . 6
1918adantr 451 . . . . 5
2016, 19nfceqdf 2488 . . . 4
2112, 20mpbid 201 . . 3
2221ex 423 . 2
234, 22impbid2 195 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540  wnf 1544   wceq 1642   wcel 1710  wnfc 2476  csn 3737  cuni 3891 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 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  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-ral 2619  df-rex 2620  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-sn 3741  df-pr 3742  df-uni 3892 This theorem is referenced by: (None)
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