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Theorem nfsbc1d 3063
 Description: Deduction version of nfsbc1 3064. (Contributed by NM, 23-May-2006.) (Revised by Mario Carneiro, 12-Oct-2016.)
Hypothesis
Ref Expression
nfsbc1d.2 (φxA)
Assertion
Ref Expression
nfsbc1d (φ → ℲxA / xψ)

Proof of Theorem nfsbc1d
StepHypRef Expression
1 df-sbc 3047 . 2 ([̣A / xψA {x ψ})
2 nfsbc1d.2 . . 3 (φxA)
3 nfab1 2491 . . . 4 x{x ψ}
43a1i 10 . . 3 (φx{x ψ})
52, 4nfeld 2504 . 2 (φ → Ⅎx A {x ψ})
61, 5nfxfrd 1571 1 (φ → ℲxA / xψ)
 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-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-sbc 3047 This theorem is referenced by:  nfsbc1  3064  nfcsb1d  3166
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