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Theorem nfmpt22 6153
Description: Bound-variable hypothesis builder for an operation in maps-to notation. (Contributed by NM, 27-Aug-2013.)
Assertion
Ref Expression
nfmpt22  |-  F/_ y
( x  e.  A ,  y  e.  B  |->  C )

Proof of Theorem nfmpt22
Dummy variable  z is distinct from all other variables.
StepHypRef Expression
1 df-mpt2 6095 . 2  |-  ( x  e.  A ,  y  e.  B  |->  C )  =  { <. <. x ,  y >. ,  z
>.  |  ( (
x  e.  A  /\  y  e.  B )  /\  z  =  C
) }
2 nfoprab2 6135 . 2  |-  F/_ y { <. <. x ,  y
>. ,  z >.  |  ( ( x  e.  A  /\  y  e.  B )  /\  z  =  C ) }
31, 2nfcxfr 2574 1  |-  F/_ y
( x  e.  A ,  y  e.  B  |->  C )
Colors of variables: wff setvar class
Syntax hints:    /\ wa 369    = wceq 1364    e. wcel 1761   F/_wnfc 2564   {coprab 6091    e. cmpt2 6092
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1713  ax-7 1733  ax-10 1780  ax-11 1785  ax-12 1797  ax-13 1948  ax-ext 2422
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1592  df-nf 1595  df-sb 1706  df-clab 2428  df-cleq 2434  df-clel 2437  df-nfc 2566  df-oprab 6094  df-mpt2 6095
This theorem is referenced by:  ovmpt2s  6213  ov2gf  6214  ovmpt2dxf  6215  ovmpt2df  6221  ovmpt2dv2  6223  xpcomco  7397  mapxpen  7473  pwfseqlem2  8822  pwfseqlem4a  8824  pwfseqlem4  8825  gsum2d2lem  16455  gsum2d2  16456  gsumcom2  16457  dprd2d2  16533  cnmpt21  19203  cnmpt2t  19205  cnmptcom  19210  cnmpt2k  19220  xkocnv  19346  fmuldfeq  29689  ovmpt2rdxf  30653
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