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Theorem bnj562 29349
Description: Technical lemma for bnj852 29366. 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
bnj562.18  |-  ( si  <->  ( m  e.  D  /\  n  =  suc  m  /\  p  e.  m )
)
bnj562.19  |-  ( et  <->  ( m  e.  D  /\  n  =  suc  m  /\  p  e.  om  /\  m  =  suc  p ) )
bnj562.38  |-  ( ( R  FrSe  A  /\  ta  /\  si )  ->  ph" )
Assertion
Ref Expression
bnj562  |-  ( ( R  FrSe  A  /\  ta  /\  et )  ->  ph" )

Proof of Theorem bnj562
StepHypRef Expression
1 bnj562.18 . . 3  |-  ( si  <->  ( m  e.  D  /\  n  =  suc  m  /\  p  e.  m )
)
2 bnj562.19 . . 3  |-  ( et  <->  ( m  e.  D  /\  n  =  suc  m  /\  p  e.  om  /\  m  =  suc  p ) )
31, 2bnj556 29345 . 2  |-  ( et 
->  si )
4 bnj562.38 . 2  |-  ( ( R  FrSe  A  /\  ta  /\  si )  ->  ph" )
53, 4syl3an3 1220 1  |-  ( ( R  FrSe  A  /\  ta  /\  et )  ->  ph" )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178    /\ w3a 937    = wceq 1653    e. wcel 1726   suc csuc 4586   omcom 4848    /\ w-bnj17 29124    FrSe w-bnj15 29130
This theorem is referenced by:  bnj600  29364  bnj908  29376
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-un 3327  df-sn 3822  df-suc 4590  df-bnj17 29125
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