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Theorem nf4 1868
Description: Variable is effectively not free in iff is always true or always false. (Contributed by Mario Carneiro, 24-Sep-2016.)
Assertion
Ref Expression
nf4  F/

Proof of Theorem nf4
StepHypRef Expression
1 nf2 1866 . 2  F/
2 imor 401 . 2
3 orcom 376 . . 3
4 alnex 1543 . . . 4
54orbi2i 505 . . 3
63, 5bitr4i 243 . 2
71, 2, 63bitri 262 1  F/
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wb 176   wo 357  wal 1540  wex 1541   F/wnf 1544
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-or 359  df-ex 1542  df-nf 1545
This theorem is referenced by: (None)
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