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Theorem nfmpo1 5804
 Description: Bound-variable hypothesis builder for an operation in maps-to notation. (Contributed by NM, 27-Aug-2013.)
Assertion
Ref Expression
nfmpo1 𝑥(𝑥𝐴, 𝑦𝐵𝐶)

Proof of Theorem nfmpo1
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 df-mpo 5745 . 2 (𝑥𝐴, 𝑦𝐵𝐶) = {⟨⟨𝑥, 𝑦⟩, 𝑧⟩ ∣ ((𝑥𝐴𝑦𝐵) ∧ 𝑧 = 𝐶)}
2 nfoprab1 5786 . 2 𝑥{⟨⟨𝑥, 𝑦⟩, 𝑧⟩ ∣ ((𝑥𝐴𝑦𝐵) ∧ 𝑧 = 𝐶)}
31, 2nfcxfr 2253 1 𝑥(𝑥𝐴, 𝑦𝐵𝐶)
 Colors of variables: wff set class Syntax hints:   ∧ wa 103   = wceq 1314   ∈ wcel 1463  Ⅎwnfc 2243  {coprab 5741   ∈ cmpo 5742 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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-oprab 5744  df-mpo 5745 This theorem is referenced by:  ovmpos  5860  ov2gf  5861  ovmpodxf  5862  ovmpodf  5868  ovmpodv2  5870  xpcomco  6686  mapxpen  6708  cnmpt21  12366  cnmpt2t  12368  cnmptcom  12373
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