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Theorem nfmpt1 3923
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 3893 . 2 (𝑥𝐴𝐵) = {⟨𝑥, 𝑧⟩ ∣ (𝑥𝐴𝑧 = 𝐵)}
2 nfopab1 3899 . 2 𝑥{⟨𝑥, 𝑧⟩ ∣ (𝑥𝐴𝑧 = 𝐵)}
31, 2nfcxfr 2225 1 𝑥(𝑥𝐴𝐵)
Colors of variables: wff set class
Syntax hints:  wa 102   = wceq 1289  wcel 1438  wnfc 2215  {copab 3890  cmpt 3891
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 3892  df-mpt 3893
This theorem is referenced by:  nffvmpt1  5300  fvmptss2  5363  fvmptssdm  5371  fvmptdf  5374  mpteqb  5377  fvmptf  5379  ralrnmpt  5425  rexrnmpt  5426  f1ompt  5434  f1mpt  5532  fliftfun  5557  dom2lem  6469  mapxpen  6544
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