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Theorem nfmpt22 5603
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 5548 . 2 (𝑥𝐴, 𝑦𝐵𝐶) = {⟨⟨𝑥, 𝑦⟩, 𝑧⟩ ∣ ((𝑥𝐴𝑦𝐵) ∧ 𝑧 = 𝐶)}
2 nfoprab2 5586 . 2 𝑦{⟨⟨𝑥, 𝑦⟩, 𝑧⟩ ∣ ((𝑥𝐴𝑦𝐵) ∧ 𝑧 = 𝐶)}
31, 2nfcxfr 2217 1 𝑦(𝑥𝐴, 𝑦𝐵𝐶)
Colors of variables: wff set class
Syntax hints:  wa 102   = wceq 1285  wcel 1434  wnfc 2207  {coprab 5544  cmpt2 5545
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-oprab 5547  df-mpt2 5548
This theorem is referenced by:  ovmpt2s  5655  ov2gf  5656  ovmpt2dxf  5657  ovmpt2df  5663  ovmpt2dv2  5665  xpcomco  6370
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