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Theorem hbim 1922
Description: If is not free in and , it is not free in . (Contributed by NM, 24-Jan-1993.) (Proof shortened by Mel L. 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 1918 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  A.wal 1393
This theorem is referenced by:  axi5r  2427  cleqhOLD  2573  hbral  2841  bj-cleqh  34358
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854
This theorem depends on definitions:  df-bi 185  df-ex 1613  df-nf 1617
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