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Theorem bnj1047 29319
Description: Technical lemma for bnj69 29356. 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
bnj1047.1  |-  ( rh  <->  A. j  e.  n  ( j  _E  i  ->  [. j  /  i ]. et ) )
bnj1047.2  |-  ( et'  <->  [. j  /  i ]. et )
Assertion
Ref Expression
bnj1047  |-  ( rh  <->  A. j  e.  n  ( j  _E  i  ->  et' ) )

Proof of Theorem bnj1047
StepHypRef Expression
1 bnj1047.1 . 2  |-  ( rh  <->  A. j  e.  n  ( j  _E  i  ->  [. j  /  i ]. et ) )
2 bnj1047.2 . . . 4  |-  ( et'  <->  [. j  /  i ]. et )
32imbi2i 303 . . 3  |-  ( ( j  _E  i  ->  et' )  <->  ( j  _E  i  ->  [. j  / 
i ]. et ) )
43ralbii 2580 . 2  |-  ( A. j  e.  n  (
j  _E  i  ->  et' )  <->  A. j  e.  n  ( j  _E  i  ->  [. j  /  i ]. et ) )
51, 4bitr4i 243 1  |-  ( rh  <->  A. j  e.  n  ( j  _E  i  ->  et' ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wral 2556   [.wsbc 3004   class class class wbr 4039    _E cep 4319
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-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-nf 1535  df-ral 2561
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