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Theorem 19.9tOLD 1857
 Description: Obsolete proof of 19.9t 1779 as of 30-Dec-2017. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.)(New usage is discouraged.)
Assertion
Ref Expression
19.9tOLD (Ⅎxφ → (xφφ))

Proof of Theorem 19.9tOLD
StepHypRef Expression
1 df-ex 1542 . . 3 (xφ ↔ ¬ x ¬ φ)
2 id 19 . . . . . 6 (Ⅎxφ → Ⅎxφ)
32nfnd 1791 . . . . 5 (Ⅎxφ → Ⅎx ¬ φ)
43nfrd 1763 . . . 4 (Ⅎxφ → (¬ φx ¬ φ))
54con1d 116 . . 3 (Ⅎxφ → (¬ x ¬ φφ))
61, 5syl5bi 208 . 2 (Ⅎxφ → (xφφ))
7 19.8a 1756 . 2 (φxφ)
86, 7impbid1 194 1 (Ⅎxφ → (xφφ))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → 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: (None)
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