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Theorem nf4dc 1576
 Description: Variable is effectively not free in iff is always true or always false, given a decidability condition. The reverse direction, nf4r 1577, holds for all propositions. (Contributed by Jim Kingdon, 21-Jul-2018.)
Assertion
Ref Expression
nf4dc DECID

Proof of Theorem nf4dc
StepHypRef Expression
1 nf2 1574 . . 3
2 imordc 807 . . 3 DECID
31, 2syl5bb 185 . 2 DECID
4 orcom 657 . . 3
5 alnex 1404 . . . 4
65orbi2i 689 . . 3
74, 6bitr4i 180 . 2
83, 7syl6bb 189 1 DECID
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 102   wo 639  DECID wdc 753  wal 1257  wnf 1365  wex 1397 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640  ax-5 1352  ax-gen 1354  ax-ie2 1399  ax-4 1416  ax-ial 1443 This theorem depends on definitions:  df-bi 114  df-dc 754  df-tru 1262  df-fal 1265  df-nf 1366 This theorem is referenced by: (None)
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