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Theorem nfmpo2 7292
Description: Bound-variable hypothesis builder for an operation in maps-to notation. (Contributed by NM, 27-Aug-2013.)
Assertion
Ref Expression
nfmpo2 𝑦(𝑥𝐴, 𝑦𝐵𝐶)

Proof of Theorem nfmpo2
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 df-mpo 7218 . 2 (𝑥𝐴, 𝑦𝐵𝐶) = {⟨⟨𝑥, 𝑦⟩, 𝑧⟩ ∣ ((𝑥𝐴𝑦𝐵) ∧ 𝑧 = 𝐶)}
2 nfoprab2 7273 . 2 𝑦{⟨⟨𝑥, 𝑦⟩, 𝑧⟩ ∣ ((𝑥𝐴𝑦𝐵) ∧ 𝑧 = 𝐶)}
31, 2nfcxfr 2902 1 𝑦(𝑥𝐴, 𝑦𝐵𝐶)
Colors of variables: wff setvar class
Syntax hints:  wa 399   = wceq 1543  wcel 2110  wnfc 2884  {coprab 7214  cmpo 7215
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2158  ax-12 2175  ax-ext 2708
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-ex 1788  df-nf 1792  df-sb 2071  df-clab 2715  df-cleq 2729  df-clel 2816  df-nfc 2886  df-oprab 7217  df-mpo 7218
This theorem is referenced by:  ovmpos  7357  ov2gf  7358  ovmpodxf  7359  ovmpodf  7365  ovmpodv2  7367  xpcomco  8735  mapxpen  8812  pwfseqlem2  10273  pwfseqlem4a  10275  pwfseqlem4  10276  gsum2d2lem  19358  gsum2d2  19359  gsumcom2  19360  dprd2d2  19431  cnmpt21  22568  cnmpt2t  22570  cnmptcom  22575  cnmpt2k  22585  xkocnv  22711  finxpreclem2  35298  finxpreclem6  35304  mnringmulrcld  41519  fmuldfeq  42799  smflimlem6  43983  ovmpordxf  45347
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