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Theorem nfmpt22 6082
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 6027 . 2  |-  ( x  e.  A ,  y  e.  B  |->  C )  =  { <. <. x ,  y >. ,  z
>.  |  ( (
x  e.  A  /\  y  e.  B )  /\  z  =  C
) }
2 nfoprab2 6065 . 2  |-  F/_ y { <. <. x ,  y
>. ,  z >.  |  ( ( x  e.  A  /\  y  e.  B )  /\  z  =  C ) }
31, 2nfcxfr 2522 1  |-  F/_ y
( x  e.  A ,  y  e.  B  |->  C )
Colors of variables: wff set class
Syntax hints:    /\ wa 359    = wceq 1649    e. wcel 1717   F/_wnfc 2512   {coprab 6023    e. cmpt2 6024
This theorem is referenced by:  ovmpt2s  6138  ov2gf  6139  ovmpt2dxf  6140  ovmpt2df  6146  ovmpt2dv2  6148  xpcomco  7136  mapxpen  7211  pwfseqlem2  8469  pwfseqlem4a  8471  pwfseqlem4  8472  gsum2d2lem  15476  gsum2d2  15477  gsumcom2  15478  dprd2d2  15531  cnmpt21  17626  cnmpt2t  17628  cnmptcom  17633  cnmpt2k  17643  xkocnv  17769  fmuldfeq  27383
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-oprab 6026  df-mpt2 6027
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