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Theorem nfmpt22 5666
Description: Bound-variable hypothesis builder for an operation in maps-to notation. (Contributed by NM, 27-Aug-2013.)
Assertion
Ref Expression
nfmpt22 𝑦(𝑥𝐴, 𝑦𝐵𝐶)

Proof of Theorem nfmpt22
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 df-mpt2 5611 . 2 (𝑥𝐴, 𝑦𝐵𝐶) = {⟨⟨𝑥, 𝑦⟩, 𝑧⟩ ∣ ((𝑥𝐴𝑦𝐵) ∧ 𝑧 = 𝐶)}
2 nfoprab2 5649 . 2 𝑦{⟨⟨𝑥, 𝑦⟩, 𝑧⟩ ∣ ((𝑥𝐴𝑦𝐵) ∧ 𝑧 = 𝐶)}
31, 2nfcxfr 2222 1 𝑦(𝑥𝐴, 𝑦𝐵𝐶)
Colors of variables: wff set class
Syntax hints:  wa 102   = wceq 1287  wcel 1436  wnfc 2212  {coprab 5607  cmpt2 5608
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-oprab 5610  df-mpt2 5611
This theorem is referenced by:  ovmpt2s  5718  ov2gf  5719  ovmpt2dxf  5720  ovmpt2df  5726  ovmpt2dv2  5728  xpcomco  6487  mapxpen  6509
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