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Theorem wl-nannan 33628
Description: Lemma for handling nested 'nand's. (Contributed by Jeff Hoffman, 19-Nov-2007.) (Revised by Wolf Lammen, 26-Jun-2020.)
Assertion
Ref Expression
wl-nannan ((𝜑 ⊼ (𝜓𝜒)) ↔ (𝜑 → (𝜓𝜒)))

Proof of Theorem wl-nannan
StepHypRef Expression
1 wl-dfnan2 33626 . 2 ((𝜑 ⊼ (𝜓𝜒)) ↔ (𝜑 → ¬ (𝜓𝜒)))
2 nanan 1596 . . 3 ((𝜓𝜒) ↔ ¬ (𝜓𝜒))
32imbi2i 325 . 2 ((𝜑 → (𝜓𝜒)) ↔ (𝜑 → ¬ (𝜓𝜒)))
41, 3bitr4i 267 1 ((𝜑 ⊼ (𝜓𝜒)) ↔ (𝜑 → (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wa 382  wnan 1594
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-an 383  df-nan 1595
This theorem is referenced by: (None)
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