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Theorem nfmpt1 4028
Description: Bound-variable hypothesis builder for the maps-to notation. (Contributed by FL, 17-Feb-2008.)
Assertion
Ref Expression
nfmpt1 𝑥(𝑥𝐴𝐵)

Proof of Theorem nfmpt1
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 df-mpt 3998 . 2 (𝑥𝐴𝐵) = {⟨𝑥, 𝑧⟩ ∣ (𝑥𝐴𝑧 = 𝐵)}
2 nfopab1 4004 . 2 𝑥{⟨𝑥, 𝑧⟩ ∣ (𝑥𝐴𝑧 = 𝐵)}
31, 2nfcxfr 2279 1 𝑥(𝑥𝐴𝐵)
Colors of variables: wff set class
Syntax hints:  wa 103   = wceq 1332  wcel 1481  wnfc 2269  {copab 3995  cmpt 3996
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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-opab 3997  df-mpt 3998
This theorem is referenced by:  nffvmpt1  5439  fvmptss2  5503  fvmptssdm  5512  fvmptdf  5515  mpteqb  5518  fvmptf  5520  ralrnmpt  5569  rexrnmpt  5570  f1ompt  5578  f1mpt  5679  fliftfun  5704  dom2lem  6673  mapxpen  6749  mkvprop  7039  cc3  7099  nfcprod1  11354  cnmpt11  12489
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