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Theorem nfsbc1d 2774
Description: Deduction version of nfsbc1 2775. (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 2759 . 2 ([A / x]ψA {xψ})
2 nfsbc1d.2 . . 3 (φxA)
3 nfab1 2177 . . . 4 x{xψ}
43a1i 9 . . 3 (φx{xψ})
52, 4nfeld 2190 . 2 (φ → Ⅎx A {xψ})
61, 5nfxfrd 1361 1 (φ → Ⅎx[A / x]ψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1346   wcel 1390  {cab 2023  wnfc 2162  [wsbc 2758
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 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-sbc 2759
This theorem is referenced by:  nfsbc1  2775  nfcsb1d  2874
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