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Theorem nfmpt22 5572
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 5517 . 2  |-  ( x  e.  A ,  y  e.  B  |->  C )  =  { <. <. x ,  y >. ,  z
>.  |  ( (
x  e.  A  /\  y  e.  B )  /\  z  =  C
) }
2 nfoprab2 5555 . 2  |-  F/_ y { <. <. x ,  y
>. ,  z >.  |  ( ( x  e.  A  /\  y  e.  B )  /\  z  =  C ) }
31, 2nfcxfr 2175 1  |-  F/_ y
( x  e.  A ,  y  e.  B  |->  C )
Colors of variables: wff set class
Syntax hints:    /\ wa 97    = wceq 1243    e. wcel 1393   F/_wnfc 2165   {coprab 5513    |-> cmpt2 5514
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-oprab 5516  df-mpt2 5517
This theorem is referenced by:  ovmpt2s  5624  ov2gf  5625  ovmpt2dxf  5626  ovmpt2df  5632  ovmpt2dv2  5634  xpcomco  6300
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