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Theorem cbvoprab12v 5921
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 1605 . 2  |-  F/ w ph
2 nfv 1605 . 2  |-  F/ v
ph
3 nfv 1605 . 2  |-  F/ x ps
4 nfv 1605 . 2  |-  F/ y ps
5 cbvoprab12v.1 . 2  |-  ( ( x  =  w  /\  y  =  v )  ->  ( ph  <->  ps )
)
61, 2, 3, 4, 5cbvoprab12 5920 1  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { <. <. w ,  v >. ,  z
>.  |  ps }
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358    = wceq 1623   {coprab 5859
This theorem is referenced by:  cpnnen  12507
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-opab 4078  df-oprab 5862
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