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Theorem bj-nfcf 31539
 Description: Version of df-nfc 2583 with a dv condition replaced with a non-freeness hypothesis. (Contributed by BJ, 2-May-2019.)
Hypothesis
Ref Expression
bj-nfcf.nf
Assertion
Ref Expression
bj-nfcf
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem bj-nfcf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-nfc 2583 . 2
2 bj-nfcf.nf . . . . . 6
32nfcri 2588 . . . . 5
43nfnf 2034 . . . 4
54sb8 2255 . . 3
6 bj-sbnf 31453 . . . . 5
7 clelsb3 2559 . . . . . 6
87nfbii 1697 . . . . 5
96, 8bitri 253 . . . 4
109albii 1693 . . 3
115, 10bitri 253 . 2
121, 11bitri 253 1
 Colors of variables: wff setvar class Syntax hints:   wb 188  wal 1444  wnf 1669  wsb 1799   wcel 1889  wnfc 2581 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-10 1917  ax-11 1922  ax-12 1935  ax-13 2093  ax-ext 2433 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-ex 1666  df-nf 1670  df-sb 1800  df-cleq 2446  df-clel 2449  df-nfc 2583 This theorem is referenced by: (None)
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