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Theorem nfmpt21 5599
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 5545 . 2  |-  ( x  e.  A ,  y  e.  B  |->  C )  =  { <. <. x ,  y >. ,  z
>.  |  ( (
x  e.  A  /\  y  e.  B )  /\  z  =  C
) }
2 nfoprab1 5582 . 2  |-  F/_ x { <. <. x ,  y
>. ,  z >.  |  ( ( x  e.  A  /\  y  e.  B )  /\  z  =  C ) }
31, 2nfcxfr 2191 1  |-  F/_ x
( x  e.  A ,  y  e.  B  |->  C )
Colors of variables: wff set class
Syntax hints:    /\ wa 101    = wceq 1259    e. wcel 1409   F/_wnfc 2181   {coprab 5541    |-> cmpt2 5542
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-oprab 5544  df-mpt2 5545
This theorem is referenced by:  ovmpt2s  5652  ov2gf  5653  ovmpt2dxf  5654  ovmpt2df  5660  ovmpt2dv2  5662  xpcomco  6331
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