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Theorem hb3an 2035
 Description: If is not free in , , and , it is not free in . (Contributed by NM, 14-Sep-2003.) (Proof shortened by Wolf Lammen, 2-Jan-2018.)
Hypotheses
Ref Expression
hb.1
hb.2
hb.3
Assertion
Ref Expression
hb3an

Proof of Theorem hb3an
StepHypRef Expression
1 hb.1 . . . 4
21nfi 1682 . . 3
3 hb.2 . . . 4
43nfi 1682 . . 3
5 hb.3 . . . 4
65nfi 1682 . . 3
72, 4, 6nf3an 2033 . 2
87nfri 1972 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   w3a 1007  wal 1450 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-12 1950 This theorem depends on definitions:  df-bi 190  df-an 378  df-3an 1009  df-ex 1672  df-nf 1676 This theorem is referenced by:  bnj982  29662  bnj1276  29698  bnj1350  29709
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