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Theorem nf4r 1650
 Description: If is always true or always false, then variable is effectively not free in . The converse holds given a decidability condition, as seen at nf4dc 1649. (Contributed by Jim Kingdon, 21-Jul-2018.)
Assertion
Ref Expression
nf4r

Proof of Theorem nf4r
StepHypRef Expression
1 orcom 718 . . 3
2 alnex 1476 . . . 4
32orbi2i 752 . . 3
41, 3bitr4i 186 . 2
5 imorr 711 . . 3
6 nf2 1647 . . 3
75, 6sylibr 133 . 2
84, 7sylbir 134 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wo 698  wal 1330  wnf 1437  wex 1469 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-gen 1426  ax-ie2 1471  ax-4 1488  ax-ial 1515 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-fal 1338  df-nf 1438 This theorem is referenced by: (None)
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