Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  hban Structured version   Visualization version   Unicode version

Theorem hban 2014
 Description: If is not free in and , it is not free in . (Contributed by NM, 14-May-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 1674 . . 3
3 hb.2 . . . 4
43nfi 1674 . . 3
52, 4nfan 2011 . 2
65nfri 1952 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 371  wal 1442 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-12 1933 This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664  df-nf 1668 This theorem is referenced by:  bnj982  29590  bnj1351  29638  bnj1352  29639  bnj1441  29652  dvelimf-o  32500  ax12indalem  32516  ax12inda2ALT  32517  hbimpg  36921  hbimpgVD  37301
 Copyright terms: Public domain W3C validator