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Theorem nfsbc 3067
 Description: Bound-variable hypothesis builder for class substitution. (Contributed by NM, 7-Sep-2014.) (Revised by Mario Carneiro, 12-Oct-2016.)
Hypotheses
Ref Expression
nfsbc.1 xA
nfsbc.2 xφ
Assertion
Ref Expression
nfsbc xA / yφ

Proof of Theorem nfsbc
StepHypRef Expression
1 nftru 1554 . . 3 y
2 nfsbc.1 . . . 4 xA
32a1i 10 . . 3 ( ⊤ → xA)
4 nfsbc.2 . . . 4 xφ
54a1i 10 . . 3 ( ⊤ → Ⅎxφ)
61, 3, 5nfsbcd 3066 . 2 ( ⊤ → ℲxA / yφ)
76trud 1323 1 xA / yφ
 Colors of variables: wff setvar class Syntax hints:   ⊤ wtru 1316  Ⅎwnf 1544  Ⅎwnfc 2476  [̣wsbc 3046 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 This theorem is referenced by:  cbvralcsf  3198  opelopabf  4711
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