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Theorem bnj589 32205
Description: Technical lemma for bnj852 32217. 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 32179 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 setvar class
Syntax hints:    -> wi 4    <-> wb 184    = wceq 1370    e. wcel 1758   A.wral 2795   U_ciun 4272   suc csuc 4822   ` cfv 5519   omcom 6579    predc-bnj14 31979
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ral 2800  df-rex 2801  df-rab 2804  df-v 3073  df-dif 3432  df-un 3434  df-in 3436  df-ss 3443  df-nul 3739  df-if 3893  df-sn 3979  df-pr 3981  df-op 3985  df-uni 4193  df-iun 4274  df-br 4394  df-suc 4826  df-iota 5482  df-fv 5527
This theorem is referenced by:  bnj594  32208  bnj1128  32284  bnj1145  32287
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