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Theorem nfmpo2 5921
Description: Bound-variable hypothesis builder for an operation in maps-to notation. (Contributed by NM, 27-Aug-2013.)
Assertion
Ref Expression
nfmpo2  |-  F/_ y
( x  e.  A ,  y  e.  B  |->  C )

Proof of Theorem nfmpo2
Dummy variable  z is distinct from all other variables.
StepHypRef Expression
1 df-mpo 5858 . 2  |-  ( x  e.  A ,  y  e.  B  |->  C )  =  { <. <. x ,  y >. ,  z
>.  |  ( (
x  e.  A  /\  y  e.  B )  /\  z  =  C
) }
2 nfoprab2 5903 . 2  |-  F/_ y { <. <. x ,  y
>. ,  z >.  |  ( ( x  e.  A  /\  y  e.  B )  /\  z  =  C ) }
31, 2nfcxfr 2309 1  |-  F/_ y
( x  e.  A ,  y  e.  B  |->  C )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    = wceq 1348    e. wcel 2141   F/_wnfc 2299   {coprab 5854    e. cmpo 5855
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-oprab 5857  df-mpo 5858
This theorem is referenced by:  ovmpos  5976  ov2gf  5977  ovmpodxf  5978  ovmpodf  5984  ovmpodv2  5986  xpcomco  6804  mapxpen  6826  cnmpt21  13085  cnmpt2t  13087  cnmptcom  13092
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