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Theorem hbn 1732
 Description: If is not free in , it is not free in . (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
hbn.1
Assertion
Ref Expression
hbn

Proof of Theorem hbn
StepHypRef Expression
1 sp 1728 . . 3
21con3i 127 . 2
3 hbn1 1716 . . 3
4 hbn.1 . . . 4
54con3i 127 . . 3
63, 5alrimih 1555 . 2
72, 6syl 15 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1530 This theorem is referenced by:  spimeh  1734  hbim  1737  hbex  1745  hban  1748  cbv3hv  1749  hbnae  1908  hbnae-o  2131  vk15.4j  28590  vk15.4jVD  29006  cbv3hvNEW7  29423  hbexwAUX7  29426  hbnaewAUX7  29458  hbnaew2AUX7  29461  ax7w2AUX7  29620  ax7w6AUX7  29622  hbexOLD7  29639  hbnaeOLD7  29664  hbnae-x12  29732  equsexv-x12  29735 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
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