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Theorem 19.9t 1779
 Description: A closed version of 19.9 1783. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortended by Wolf Lammen, 30-Dec-2017.)
Assertion
Ref Expression
19.9t (Ⅎxφ → (xφφ))

Proof of Theorem 19.9t
StepHypRef Expression
1 df-nf 1545 . . 3 (Ⅎxφx(φxφ))
2 19.9ht 1778 . . 3 (x(φxφ) → (xφφ))
31, 2sylbi 187 . 2 (Ⅎxφ → (xφφ))
4 19.8a 1756 . 2 (φxφ)
53, 4impbid1 194 1 (Ⅎxφ → (xφφ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wal 1540  ∃wex 1541  Ⅎwnf 1544 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-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545 This theorem is referenced by:  19.9h  1780  19.9d  1782  19.9OLD  1784  19.21t  1795  19.23t  1800  19.23tOLD  1819  vtoclegft  2926
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