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Theorem nfoprab 5549
 Description: Bound-variable hypothesis builder for an operation class abstraction. (Contributed by NM, 22-Aug-2013.)
Hypothesis
Ref Expression
nfoprab.1 wφ
Assertion
Ref Expression
nfoprab w{x, y, z φ}
Distinct variable groups:   x,w   y,w   z,w
Allowed substitution hints:   φ(x,y,z,w)

Proof of Theorem nfoprab
Dummy variable v is distinct from all other variables.
StepHypRef Expression
1 df-oprab 5528 . 2 {x, y, z φ} = {v xyz(v = x, y, z φ)}
2 nfv 1619 . . . . . . 7 w v = x, y, z
3 nfoprab.1 . . . . . . 7 wφ
42, 3nfan 1824 . . . . . 6 w(v = x, y, z φ)
54nfex 1843 . . . . 5 wz(v = x, y, z φ)
65nfex 1843 . . . 4 wyz(v = x, y, z φ)
76nfex 1843 . . 3 wxyz(v = x, y, z φ)
87nfab 2493 . 2 w{v xyz(v = x, y, z φ)}
91, 8nfcxfr 2486 1 w{x, y, z φ}
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 358  ∃wex 1541  Ⅎwnf 1544   = wceq 1642  {cab 2339  Ⅎwnfc 2476  ⟨cop 4561  {coprab 5527 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 This theorem is referenced by:  nfmpt2  5675
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