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Theorem bnj561 29251
Description: Technical lemma for bnj852 29269. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj561.18  |-  ( si  <->  ( m  e.  D  /\  n  =  suc  m  /\  p  e.  m )
)
bnj561.19  |-  ( et  <->  ( m  e.  D  /\  n  =  suc  m  /\  p  e.  om  /\  m  =  suc  p ) )
bnj561.37  |-  ( ( R  FrSe  A  /\  ta  /\  si )  ->  G  Fn  n )
Assertion
Ref Expression
bnj561  |-  ( ( R  FrSe  A  /\  ta  /\  et )  ->  G  Fn  n )

Proof of Theorem bnj561
StepHypRef Expression
1 bnj561.18 . . 3  |-  ( si  <->  ( m  e.  D  /\  n  =  suc  m  /\  p  e.  m )
)
2 bnj561.19 . . 3  |-  ( et  <->  ( m  e.  D  /\  n  =  suc  m  /\  p  e.  om  /\  m  =  suc  p ) )
31, 2bnj556 29248 . 2  |-  ( et 
->  si )
4 bnj561.37 . 2  |-  ( ( R  FrSe  A  /\  ta  /\  si )  ->  G  Fn  n )
53, 4syl3an3 1217 1  |-  ( ( R  FrSe  A  /\  ta  /\  et )  ->  G  Fn  n )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ w3a 934    = wceq 1632    e. wcel 1696   suc csuc 4410   omcom 4672    Fn wfn 5266    /\ w-bnj17 29027    FrSe w-bnj15 29033
This theorem is referenced by:  bnj600  29267  bnj908  29279
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-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-sn 3659  df-suc 4414  df-bnj17 29028
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