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Theorem nfmpt22 6141
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 6086 . 2  |-  ( x  e.  A ,  y  e.  B  |->  C )  =  { <. <. x ,  y >. ,  z
>.  |  ( (
x  e.  A  /\  y  e.  B )  /\  z  =  C
) }
2 nfoprab2 6124 . 2  |-  F/_ y { <. <. x ,  y
>. ,  z >.  |  ( ( x  e.  A  /\  y  e.  B )  /\  z  =  C ) }
31, 2nfcxfr 2569 1  |-  F/_ y
( x  e.  A ,  y  e.  B  |->  C )
Colors of variables: wff set class
Syntax hints:    /\ wa 359    = wceq 1652    e. wcel 1725   F/_wnfc 2559   {coprab 6082    e. cmpt2 6083
This theorem is referenced by:  ovmpt2s  6197  ov2gf  6198  ovmpt2dxf  6199  ovmpt2df  6205  ovmpt2dv2  6207  xpcomco  7198  mapxpen  7273  pwfseqlem2  8534  pwfseqlem4a  8536  pwfseqlem4  8537  gsum2d2lem  15547  gsum2d2  15548  gsumcom2  15549  dprd2d2  15602  cnmpt21  17703  cnmpt2t  17705  cnmptcom  17710  cnmpt2k  17720  xkocnv  17846  fmuldfeq  27689
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-oprab 6085  df-mpt2 6086
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