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Theorem hbim 1836
 Description: If is not free in and , it is not free in . (Contributed by NM, 5-Aug-1993.) (Proof shortened by O'Cat, 3-Mar-2008.) (Proof shortened by Wolf Lammen, 1-Jan-2018.)
Hypotheses
Ref Expression
hbim.1
hbim.2
Assertion
Ref Expression
hbim

Proof of Theorem hbim
StepHypRef Expression
1 hbim.1 . 2
2 hbim.2 . . 3
32a1i 11 . 2
41, 3hbim1 1829 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1549 This theorem is referenced by:  19.23hOLD  1839  hbanOLD  1851  19.21hOLD  1862  cbv3hvOLD  1879  ax12olem5OLD  2015  axi5r  2408  cleqh  2532  hbral  2746  cbv3hvNEW7  29383 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761 This theorem depends on definitions:  df-bi 178  df-ex 1551  df-nf 1554
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