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Theorem cbvoprab12v 5846
Description: Rule used to change first two bound variables in an operation abstraction, using implicit substitution. (Contributed by NM, 8-Oct-2004.)
Hypothesis
Ref Expression
cbvoprab12v.1  |-  ( ( x  =  w  /\  y  =  v )  ->  ( ph  <->  ps )
)
Assertion
Ref Expression
cbvoprab12v  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { <. <. w ,  v >. ,  z
>.  |  ps }
Distinct variable groups:    x, y, z, w, v    ph, w, v    ps, x, y
Allowed substitution hints:    ph( x, y, z)    ps( z, w, v)

Proof of Theorem cbvoprab12v
StepHypRef Expression
1 nfv 1508 . 2  |-  F/ w ph
2 nfv 1508 . 2  |-  F/ v
ph
3 nfv 1508 . 2  |-  F/ x ps
4 nfv 1508 . 2  |-  F/ y ps
5 cbvoprab12v.1 . 2  |-  ( ( x  =  w  /\  y  =  v )  ->  ( ph  <->  ps )
)
61, 2, 3, 4, 5cbvoprab12 5845 1  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { <. <. w ,  v >. ,  z
>.  |  ps }
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104    = wceq 1331   {coprab 5775
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-opab 3990  df-oprab 5778
This theorem is referenced by: (None)
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