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Theorem nfmpt1 4111
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 4081 . 2 (𝑥𝐴𝐵) = {⟨𝑥, 𝑧⟩ ∣ (𝑥𝐴𝑧 = 𝐵)}
2 nfopab1 4087 . 2 𝑥{⟨𝑥, 𝑧⟩ ∣ (𝑥𝐴𝑧 = 𝐵)}
31, 2nfcxfr 2329 1 𝑥(𝑥𝐴𝐵)
Colors of variables: wff set class
Syntax hints:  wa 104   = wceq 1364  wcel 2160  wnfc 2319  {copab 4078  cmpt 4079
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-opab 4080  df-mpt 4081
This theorem is referenced by:  nffvmpt1  5545  fvmptss2  5612  fvmptssdm  5621  fvmptdf  5624  mpteqb  5627  fvmptf  5629  ralrnmpt  5679  rexrnmpt  5680  f1ompt  5688  f1mpt  5793  fliftfun  5818  dom2lem  6798  mapxpen  6876  mkvprop  7186  cc3  7297  nfcprod1  11594  cnmpt11  14243  lgseisenlem2  14912
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