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Theorem cbvoprab12v 5937
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 1609 . 2  |-  F/ w ph
2 nfv 1609 . 2  |-  F/ v
ph
3 nfv 1609 . 2  |-  F/ x ps
4 nfv 1609 . 2  |-  F/ y ps
5 cbvoprab12v.1 . 2  |-  ( ( x  =  w  /\  y  =  v )  ->  ( ph  <->  ps )
)
61, 2, 3, 4, 5cbvoprab12 5936 1  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { <. <. w ,  v >. ,  z
>.  |  ps }
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358    = wceq 1632   {coprab 5875
This theorem is referenced by:  cpnnen  12523
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-opab 4094  df-oprab 5878
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