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Theorem bnj562 28993
Description: Technical lemma for bnj852 29010. 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 28989 . 2  |-  ( et 
->  si )
4 bnj562.38 . 2  |-  ( ( R  FrSe  A  /\  ta  /\  si )  ->  ph" )
53, 4syl3an3 1219 1  |-  ( ( R  FrSe  A  /\  ta  /\  et )  ->  ph" )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    /\ w3a 936    = wceq 1649    e. wcel 1721   suc csuc 4551   omcom 4812    /\ w-bnj17 28768    FrSe w-bnj15 28774
This theorem is referenced by:  bnj600  29008  bnj908  29020
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-v 2926  df-un 3293  df-sn 3788  df-suc 4555  df-bnj17 28769
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