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Theorem nfsab 2345
 Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfsab.1 xφ
Assertion
Ref Expression
nfsab x z {y φ}
Distinct variable group:   x,z
Allowed substitution hints:   φ(x,y,z)

Proof of Theorem nfsab
StepHypRef Expression
1 nfsab.1 . . . 4 xφ
21nfri 1762 . . 3 (φxφ)
32hbab 2344 . 2 (z {y φ} → x z {y φ})
43nfi 1551 1 x z {y φ}
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnf 1544   ∈ wcel 1710  {cab 2339 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 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 This theorem is referenced by:  nfab  2493
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