MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nannanOLD Structured version   Visualization version   GIF version

Theorem nannanOLD 1617
Description: Obsolete proof of nannan 1616 as of 19-Oct-2022. (Contributed by Jeff Hoffman, 19-Nov-2007.) (Proof shortened by Wolf Lammen, 7-Mar-2020.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nannanOLD ((𝜑 ⊼ (𝜓𝜒)) ↔ (𝜑 → (𝜓𝜒)))

Proof of Theorem nannanOLD
StepHypRef Expression
1 imnan 389 . 2 ((𝜑 → ¬ (𝜓𝜒)) ↔ ¬ (𝜑 ∧ (𝜓𝜒)))
2 nanan 1611 . . 3 ((𝜓𝜒) ↔ ¬ (𝜓𝜒))
32imbi2i 328 . 2 ((𝜑 → (𝜓𝜒)) ↔ (𝜑 → ¬ (𝜓𝜒)))
4 df-nan 1610 . 2 ((𝜑 ⊼ (𝜓𝜒)) ↔ ¬ (𝜑 ∧ (𝜓𝜒)))
51, 3, 43bitr4ri 296 1 ((𝜑 ⊼ (𝜓𝜒)) ↔ (𝜑 → (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 198  wa 385  wnan 1609
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 199  df-an 386  df-nan 1610
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator