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Theorem hban 1828
Description: If is not free in and , it is not free in . (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 2-Jan-2018.)
Hypotheses
Ref Expression
hb.1
hb.2
Assertion
Ref Expression
hban

Proof of Theorem hban
StepHypRef Expression
1 hb.1 . . . 4
21nfi 1551 . . 3  F/
3 hb.2 . . . 4
43nfi 1551 . . 3  F/
52, 4nfan 1824 . 2  F/
65nfri 1762 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wa 358  wal 1540
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-an 360  df-tru 1319  df-ex 1542  df-nf 1545
This theorem is referenced by:  hb3anOLD  1831  dvelimv  1939  dvelimh  1964  dvelimALT  2133  dvelimf-o  2180  ax11indalem  2197  ax11inda2ALT  2198  cleqh  2450  hboprab  5562
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