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Theorem nfoprab1 5546
 Description: The abstraction variables in an operation class abstraction are not free. (Contributed by NM, 25-Apr-1995.) (Revised by David Abernethy, 19-Jun-2012.)
Assertion
Ref Expression
nfoprab1 x{x, y, z φ}

Proof of Theorem nfoprab1
Dummy variable w is distinct from all other variables.
StepHypRef Expression
1 df-oprab 5528 . 2 {x, y, z φ} = {w xyz(w = x, y, z φ)}
2 nfe1 1732 . . 3 xxyz(w = x, y, z φ)
32nfab 2493 . 2 x{w xyz(w = x, y, z φ)}
41, 3nfcxfr 2486 1 x{x, y, z φ}
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 358  ∃wex 1541   = wceq 1642  {cab 2339  Ⅎwnfc 2476  ⟨cop 4561  {coprab 5527 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 This theorem is referenced by:  ov3  5599  nfmpt21  5673
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