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Theorem nfcsb1d 2874
Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by Mario Carneiro, 12-Oct-2016.)
Hypothesis
Ref Expression
nfcsb1d.1 (φxA)
Assertion
Ref Expression
nfcsb1d (φxA / xB)

Proof of Theorem nfcsb1d
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 df-csb 2847 . 2 A / xB = {y[A / x]y B}
2 nfv 1418 . . 3 yφ
3 nfcsb1d.1 . . . 4 (φxA)
43nfsbc1d 2774 . . 3 (φ → Ⅎx[A / x]y B)
52, 4nfabd 2193 . 2 (φx{y[A / x]y B})
61, 5nfcxfrd 2173 1 (φxA / xB)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1390  {cab 2023  wnfc 2162  [wsbc 2758  csb 2846
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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  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  df-csb 2847
This theorem is referenced by:  nfcsb1  2875
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