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Theorem nfmpo2 5883
 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 5823 . 2 (𝑥𝐴, 𝑦𝐵𝐶) = {⟨⟨𝑥, 𝑦⟩, 𝑧⟩ ∣ ((𝑥𝐴𝑦𝐵) ∧ 𝑧 = 𝐶)}
2 nfoprab2 5865 . 2 𝑦{⟨⟨𝑥, 𝑦⟩, 𝑧⟩ ∣ ((𝑥𝐴𝑦𝐵) ∧ 𝑧 = 𝐶)}
31, 2nfcxfr 2296 1 𝑦(𝑥𝐴, 𝑦𝐵𝐶)
 Colors of variables: wff set class Syntax hints:   ∧ wa 103   = wceq 1335   ∈ wcel 2128  Ⅎwnfc 2286  {coprab 5819   ∈ cmpo 5820 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-oprab 5822  df-mpo 5823 This theorem is referenced by:  ovmpos  5938  ov2gf  5939  ovmpodxf  5940  ovmpodf  5946  ovmpodv2  5948  xpcomco  6764  mapxpen  6786  cnmpt21  12651  cnmpt2t  12653  cnmptcom  12658
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