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Theorem nfmpt1 3961
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 3931 . 2 (𝑥𝐴𝐵) = {⟨𝑥, 𝑧⟩ ∣ (𝑥𝐴𝑧 = 𝐵)}
2 nfopab1 3937 . 2 𝑥{⟨𝑥, 𝑧⟩ ∣ (𝑥𝐴𝑧 = 𝐵)}
31, 2nfcxfr 2237 1 𝑥(𝑥𝐴𝐵)
Colors of variables: wff set class
Syntax hints:  wa 103   = wceq 1299  wcel 1448  wnfc 2227  {copab 3928  cmpt 3929
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082
This theorem depends on definitions:  df-bi 116  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-opab 3930  df-mpt 3931
This theorem is referenced by:  nffvmpt1  5364  fvmptss2  5428  fvmptssdm  5437  fvmptdf  5440  mpteqb  5443  fvmptf  5445  ralrnmpt  5494  rexrnmpt  5495  f1ompt  5503  f1mpt  5604  fliftfun  5629  dom2lem  6596  mapxpen  6671  mkvprop  6943  cnmpt11  12233
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