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Theorem nfcsb1d 3166
 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 (φx[A / x]B)

Proof of Theorem nfcsb1d
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 df-csb 3137 . 2 [A / x]B = {y A / xy B}
2 nfv 1619 . . 3 yφ
3 nfcsb1d.1 . . . 4 (φxA)
43nfsbc1d 3063 . . 3 (φ → ℲxA / xy B)
52, 4nfabd 2508 . 2 (φx{y A / xy B})
61, 5nfcxfrd 2487 1 (φx[A / x]B)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1710  {cab 2339  Ⅎwnfc 2476  [̣wsbc 3046  [csb 3136 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  df-csb 3137 This theorem is referenced by:  nfcsb1  3167
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