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Theorem nfndOLD 1792
 Description: Obsolete proof of nfnd 1791 as of 28-Dec-2017. (Contributed by Mario Carneiro, 24-Sep-2016.) (New usage is discouraged.)
Hypothesis
Ref Expression
nfnd.1 (φ → Ⅎxψ)
Assertion
Ref Expression
nfndOLD (φ → Ⅎx ¬ ψ)

Proof of Theorem nfndOLD
StepHypRef Expression
1 nfnd.1 . 2 (φ → Ⅎxψ)
2 nfnf1 1790 . . 3 xxψ
3 ax6o 1750 . . . . 5 x ¬ xψψ)
43con1i 121 . . . 4 ψx ¬ xψ)
5 df-nf 1545 . . . . 5 (Ⅎxψx(ψxψ))
6 con3 126 . . . . . 6 ((ψxψ) → (¬ xψ → ¬ ψ))
76al2imi 1561 . . . . 5 (x(ψxψ) → (x ¬ xψx ¬ ψ))
85, 7sylbi 187 . . . 4 (Ⅎxψ → (x ¬ xψx ¬ ψ))
94, 8syl5 28 . . 3 (Ⅎxψ → (¬ ψx ¬ ψ))
102, 9nfd 1766 . 2 (Ⅎxψ → Ⅎx ¬ ψ)
111, 10syl 15 1 (φ → Ⅎx ¬ ψ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540  Ⅎwnf 1544 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-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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