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Theorem cbvoprab12v 6246
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 1674 . 2  |-  F/ w ph
2 nfv 1674 . 2  |-  F/ v
ph
3 nfv 1674 . 2  |-  F/ x ps
4 nfv 1674 . 2  |-  F/ y ps
5 cbvoprab12v.1 . 2  |-  ( ( x  =  w  /\  y  =  v )  ->  ( ph  <->  ps )
)
61, 2, 3, 4, 5cbvoprab12 6245 1  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { <. <. w ,  v >. ,  z
>.  |  ps }
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ wa 369    = wceq 1370   {coprab 6177
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 1709  ax-7 1729  ax-9 1761  ax-10 1776  ax-11 1781  ax-12 1793  ax-13 1944  ax-ext 2429  ax-sep 4497  ax-nul 4505  ax-pr 4615
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 1702  df-clab 2436  df-cleq 2442  df-clel 2445  df-nfc 2598  df-ne 2643  df-rab 2801  df-v 3056  df-dif 3415  df-un 3417  df-in 3419  df-ss 3426  df-nul 3722  df-if 3876  df-sn 3962  df-pr 3964  df-op 3968  df-opab 4435  df-oprab 6180
This theorem is referenced by:  cpnnen  13599
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