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Theorem nfmpt21 6359
Description: Bound-variable hypothesis builder for an operation in maps-to notation. (Contributed by NM, 27-Aug-2013.)
Assertion
Ref Expression
nfmpt21  |-  F/_ x
( x  e.  A ,  y  e.  B  |->  C )

Proof of Theorem nfmpt21
Dummy variable  z is distinct from all other variables.
StepHypRef Expression
1 df-mpt2 6300 . 2  |-  ( x  e.  A ,  y  e.  B  |->  C )  =  { <. <. x ,  y >. ,  z
>.  |  ( (
x  e.  A  /\  y  e.  B )  /\  z  =  C
) }
2 nfoprab1 6341 . 2  |-  F/_ x { <. <. x ,  y
>. ,  z >.  |  ( ( x  e.  A  /\  y  e.  B )  /\  z  =  C ) }
31, 2nfcxfr 2627 1  |-  F/_ x
( x  e.  A ,  y  e.  B  |->  C )
Colors of variables: wff setvar class
Syntax hints:    /\ wa 369    = wceq 1379    e. wcel 1767   F/_wnfc 2615   {coprab 6296    |-> cmpt2 6297
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-oprab 6299  df-mpt2 6300
This theorem is referenced by:  ovmpt2s  6421  ov2gf  6422  ovmpt2dxf  6423  ovmpt2df  6429  ovmpt2dv2  6431  xpcomco  7619  mapxpen  7695  pwfseqlem2  9049  pwfseqlem4a  9051  pwfseqlem4  9052  gsum2d2lem  16874  gsum2d2  16875  gsumcom2  16876  dprd2d2  16965  cnmpt21  20040  cnmpt2t  20042  cnmptcom  20047  cnmpt2k  20057  xkocnv  20183  fmuldfeqlem1  31446  fmuldfeq  31447  ovmpt2rdxf  32362
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