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Theorem nfmpt21 5673
 Description: Bound-variable hypothesis builder for an operation in maps-to notation. (Contributed by NM, 27-Aug-2013.)
Assertion
Ref Expression
nfmpt21 x(x A, y B C)

Proof of Theorem nfmpt21
Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 df-mpt2 5654 . 2 (x A, y B C) = {x, y, z ((x A y B) z = C)}
2 nfoprab1 5546 . 2 x{x, y, z ((x A y B) z = C)}
31, 2nfcxfr 2486 1 x(x A, y B C)
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 358   = wceq 1642   ∈ wcel 1710  Ⅎwnfc 2476  {coprab 5527   ↦ cmpt2 5653 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-oprab 5528  df-mpt2 5654 This theorem is referenced by:  ov2gf  5711
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