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Theorem nfmpt22 5597
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 5542 . 2 (𝑥𝐴, 𝑦𝐵𝐶) = {⟨⟨𝑥, 𝑦⟩, 𝑧⟩ ∣ ((𝑥𝐴𝑦𝐵) ∧ 𝑧 = 𝐶)}
2 nfoprab2 5580 . 2 𝑦{⟨⟨𝑥, 𝑦⟩, 𝑧⟩ ∣ ((𝑥𝐴𝑦𝐵) ∧ 𝑧 = 𝐶)}
31, 2nfcxfr 2189 1 𝑦(𝑥𝐴, 𝑦𝐵𝐶)
Colors of variables: wff set class
Syntax hints:  wa 101   = wceq 1257  wcel 1407  wnfc 2179  {coprab 5538  cmpt2 5539
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 638  ax-5 1350  ax-7 1351  ax-gen 1352  ax-ie1 1396  ax-ie2 1397  ax-8 1409  ax-10 1410  ax-11 1411  ax-i12 1412  ax-bndl 1413  ax-4 1414  ax-17 1433  ax-i9 1437  ax-ial 1441  ax-i5r 1442  ax-ext 2036
This theorem depends on definitions:  df-bi 114  df-nf 1364  df-sb 1660  df-clab 2041  df-cleq 2047  df-clel 2050  df-nfc 2181  df-oprab 5541  df-mpt2 5542
This theorem is referenced by:  ovmpt2s  5649  ov2gf  5650  ovmpt2dxf  5651  ovmpt2df  5657  ovmpt2dv2  5659  xpcomco  6328
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