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Theorem nfmpt1 3879
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 3849 . 2  |-  ( x  e.  A  |->  B )  =  { <. x ,  z >.  |  ( x  e.  A  /\  z  =  B ) }
2 nfopab1 3855 . 2  |-  F/_ x { <. x ,  z
>.  |  ( x  e.  A  /\  z  =  B ) }
31, 2nfcxfr 2217 1  |-  F/_ x
( x  e.  A  |->  B )
Colors of variables: wff set class
Syntax hints:    /\ wa 102    = wceq 1285    e. wcel 1434   F/_wnfc 2207   {copab 3846    |-> cmpt 3847
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 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-opab 3848  df-mpt 3849
This theorem is referenced by:  nffvmpt1  5217  fvmptss2  5279  fvmptssdm  5287  fvmptdf  5290  mpteqb  5293  fvmptf  5295  ralrnmpt  5341  rexrnmpt  5342  f1ompt  5352  f1mpt  5442  fliftfun  5467  dom2lem  6319
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