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Theorem bnj93 28565
Description: Technical lemma for bnj97 28568. 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.)
Assertion
Ref Expression
bnj93  |-  ( ( R  FrSe  A  /\  x  e.  A )  ->  pred ( x ,  A ,  R )  e.  _V )
Distinct variable groups:    x, A    x, R

Proof of Theorem bnj93
StepHypRef Expression
1 df-bnj15 28388 . . . 4  |-  ( R 
FrSe  A  <->  ( R  Fr  A  /\  R  Se  A
) )
21simprbi 451 . . 3  |-  ( R 
FrSe  A  ->  R  Se  A )
3 df-bnj13 28386 . . 3  |-  ( R  Se  A  <->  A. x  e.  A  pred ( x ,  A ,  R
)  e.  _V )
42, 3sylib 189 . 2  |-  ( R 
FrSe  A  ->  A. x  e.  A  pred ( x ,  A ,  R
)  e.  _V )
54r19.21bi 2740 1  |-  ( ( R  FrSe  A  /\  x  e.  A )  ->  pred ( x ,  A ,  R )  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359    e. wcel 1717   A.wral 2642   _Vcvv 2892    Fr wfr 4472    predc-bnj14 28383    Se w-bnj13 28385    FrSe w-bnj15 28387
This theorem is referenced by:  bnj96  28567  bnj97  28568  bnj149  28577  bnj150  28578  bnj518  28588  bnj1148  28696
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 1661  ax-8 1682  ax-11 1753
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-ral 2647  df-bnj13 28386  df-bnj15 28388
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