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Theorem nfsbcd 3066
 Description: Deduction version of nfsbc 3067. (Contributed by NM, 23-Nov-2005.) (Revised by Mario Carneiro, 12-Oct-2016.)
Hypotheses
Ref Expression
nfsbcd.1 yφ
nfsbcd.2 (φxA)
nfsbcd.3 (φ → Ⅎxψ)
Assertion
Ref Expression
nfsbcd (φ → ℲxA / yψ)

Proof of Theorem nfsbcd
StepHypRef Expression
1 df-sbc 3047 . 2 ([̣A / yψA {y ψ})
2 nfsbcd.2 . . 3 (φxA)
3 nfsbcd.1 . . . 4 yφ
4 nfsbcd.3 . . . 4 (φ → Ⅎxψ)
53, 4nfabd 2508 . . 3 (φx{y ψ})
62, 5nfeld 2504 . 2 (φ → Ⅎx A {y ψ})
71, 6nfxfrd 1571 1 (φ → ℲxA / yψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  Ⅎwnf 1544   ∈ wcel 1710  {cab 2339  Ⅎwnfc 2476  [̣wsbc 3046 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-sbc 3047 This theorem is referenced by:  nfsbc  3067  nfcsbd  3169  sbcnestgf  3183
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