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Theorem nfsbc1d 3420
 Description: Deduction version of nfsbc1 3421. (Contributed by NM, 23-May-2006.) (Revised by Mario Carneiro, 12-Oct-2016.)
Hypothesis
Ref Expression
nfsbc1d.2 (𝜑𝑥𝐴)
Assertion
Ref Expression
nfsbc1d (𝜑 → Ⅎ𝑥[𝐴 / 𝑥]𝜓)

Proof of Theorem nfsbc1d
StepHypRef Expression
1 df-sbc 3403 . 2 ([𝐴 / 𝑥]𝜓𝐴 ∈ {𝑥𝜓})
2 nfsbc1d.2 . . 3 (𝜑𝑥𝐴)
3 nfab1 2753 . . . 4 𝑥{𝑥𝜓}
43a1i 11 . . 3 (𝜑𝑥{𝑥𝜓})
52, 4nfeld 2759 . 2 (𝜑 → Ⅎ𝑥 𝐴 ∈ {𝑥𝜓})
61, 5nfxfrd 1772 1 (𝜑 → Ⅎ𝑥[𝐴 / 𝑥]𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  Ⅎwnf 1699   ∈ wcel 1977  {cab 2596  Ⅎwnfc 2738  [wsbc 3402 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-sbc 3403 This theorem is referenced by:  nfsbc1  3421  nfcsb1d  3513
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