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Theorem nfmpt1 3931
Description: Bound-variable hypothesis builder for the maps-to notation. (Contributed by FL, 17-Feb-2008.)
Assertion
Ref Expression
nfmpt1  |-  F/_ x
( x  e.  A  |->  B )

Proof of Theorem nfmpt1
Dummy variable  z is distinct from all other variables.
StepHypRef Expression
1 df-mpt 3901 . 2  |-  ( x  e.  A  |->  B )  =  { <. x ,  z >.  |  ( x  e.  A  /\  z  =  B ) }
2 nfopab1 3907 . 2  |-  F/_ x { <. x ,  z
>.  |  ( x  e.  A  /\  z  =  B ) }
31, 2nfcxfr 2225 1  |-  F/_ x
( x  e.  A  |->  B )
Colors of variables: wff set class
Syntax hints:    /\ wa 102    = wceq 1289    e. wcel 1438   F/_wnfc 2215   {copab 3898    |-> cmpt 3899
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-opab 3900  df-mpt 3901
This theorem is referenced by:  nffvmpt1  5316  fvmptss2  5379  fvmptssdm  5387  fvmptdf  5390  mpteqb  5393  fvmptf  5395  ralrnmpt  5441  rexrnmpt  5442  f1ompt  5450  f1mpt  5550  fliftfun  5575  dom2lem  6489  mapxpen  6564
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