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Theorem nfsbc1d 2780
 Description: Deduction version of nfsbc1 2781. (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 2765 . 2 ([𝐴 / 𝑥]𝜓𝐴 ∈ {𝑥𝜓})
2 nfsbc1d.2 . . 3 (𝜑𝑥𝐴)
3 nfab1 2180 . . . 4 𝑥{𝑥𝜓}
43a1i 9 . . 3 (𝜑𝑥{𝑥𝜓})
52, 4nfeld 2193 . 2 (𝜑 → Ⅎ𝑥 𝐴 ∈ {𝑥𝜓})
61, 5nfxfrd 1364 1 (𝜑 → Ⅎ𝑥[𝐴 / 𝑥]𝜓)
 Colors of variables: wff set class Syntax hints:   → wi 4  Ⅎwnf 1349   ∈ wcel 1393  {cab 2026  Ⅎwnfc 2165  [wsbc 2764 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-sbc 2765 This theorem is referenced by:  nfsbc1  2781  nfcsb1d  2880
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