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Theorem nfmpt22 6108
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 6053 . 2  |-  ( x  e.  A ,  y  e.  B  |->  C )  =  { <. <. x ,  y >. ,  z
>.  |  ( (
x  e.  A  /\  y  e.  B )  /\  z  =  C
) }
2 nfoprab2 6091 . 2  |-  F/_ y { <. <. x ,  y
>. ,  z >.  |  ( ( x  e.  A  /\  y  e.  B )  /\  z  =  C ) }
31, 2nfcxfr 2545 1  |-  F/_ y
( x  e.  A ,  y  e.  B  |->  C )
Colors of variables: wff set class
Syntax hints:    /\ wa 359    = wceq 1649    e. wcel 1721   F/_wnfc 2535   {coprab 6049    e. cmpt2 6050
This theorem is referenced by:  ovmpt2s  6164  ov2gf  6165  ovmpt2dxf  6166  ovmpt2df  6172  ovmpt2dv2  6174  xpcomco  7165  mapxpen  7240  pwfseqlem2  8498  pwfseqlem4a  8500  pwfseqlem4  8501  gsum2d2lem  15510  gsum2d2  15511  gsumcom2  15512  dprd2d2  15565  cnmpt21  17664  cnmpt2t  17666  cnmptcom  17671  cnmpt2k  17681  xkocnv  17807  fmuldfeq  27588
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 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
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 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-oprab 6052  df-mpt2 6053
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