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Theorem nfbidOLD 1833
 Description: Obsolete proof of nfbid 1832 as of 29-Dec-2017. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfbid.1 (φ → Ⅎxψ)
nfbid.2 (φ → Ⅎxχ)
Assertion
Ref Expression
nfbidOLD (φ → Ⅎx(ψχ))

Proof of Theorem nfbidOLD
StepHypRef Expression
1 dfbi1 184 . 2 ((ψχ) ↔ ¬ ((ψχ) → ¬ (χψ)))
2 nfbid.1 . . . . 5 (φ → Ⅎxψ)
3 nfbid.2 . . . . 5 (φ → Ⅎxχ)
42, 3nfimd 1808 . . . 4 (φ → Ⅎx(ψχ))
53, 2nfimd 1808 . . . . 5 (φ → Ⅎx(χψ))
65nfnd 1791 . . . 4 (φ → Ⅎx ¬ (χψ))
74, 6nfimd 1808 . . 3 (φ → Ⅎx((ψχ) → ¬ (χψ)))
87nfnd 1791 . 2 (φ → Ⅎx ¬ ((ψχ) → ¬ (χψ)))
91, 8nfxfrd 1571 1 (φ → Ⅎx(ψχ))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176  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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