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Theorem bnj589 29378
Description: Technical lemma for bnj852 29390. 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.)
Hypothesis
Ref Expression
bnj589.1  |-  ( ps  <->  A. i  e.  om  ( suc  i  e.  n  ->  ( f `  suc  i )  =  U_ y  e.  ( f `  i )  pred (
y ,  A ,  R ) ) )
Assertion
Ref Expression
bnj589  |-  ( ps  <->  A. k  e.  om  ( suc  k  e.  n  ->  ( f `  suc  k )  =  U_ y  e.  ( f `  k )  pred (
y ,  A ,  R ) ) )
Distinct variable groups:    A, i,
k    R, i, k    f,
i, k, y    i, n, k
Allowed substitution hints:    ps( y, f, i, k, n)    A( y, f, n)    R( y,
f, n)

Proof of Theorem bnj589
StepHypRef Expression
1 bnj589.1 . 2  |-  ( ps  <->  A. i  e.  om  ( suc  i  e.  n  ->  ( f `  suc  i )  =  U_ y  e.  ( f `  i )  pred (
y ,  A ,  R ) ) )
21bnj222 29352 1  |-  ( ps  <->  A. k  e.  om  ( suc  k  e.  n  ->  ( f `  suc  k )  =  U_ y  e.  ( f `  k )  pred (
y ,  A ,  R ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178    = wceq 1653    e. wcel 1727   A.wral 2711   U_ciun 4117   suc csuc 4612   omcom 4874   ` cfv 5483    predc-bnj14 29150
This theorem is referenced by:  bnj594  29381  bnj1128  29457  bnj1145  29460
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 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423
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 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ral 2716  df-rex 2717  df-rab 2720  df-v 2964  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-uni 4040  df-iun 4119  df-br 4238  df-suc 4616  df-iota 5447  df-fv 5491
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