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Theorem nanbi1OLD 1623
 Description: Obsolete proof of nanbi1 1622 as of 19-Oct-2022. (Contributed by Anthony Hart, 1-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nanbi1OLD ((𝜑𝜓) → ((𝜑𝜒) ↔ (𝜓𝜒)))

Proof of Theorem nanbi1OLD
StepHypRef Expression
1 anbi1 626 . . 3 ((𝜑𝜓) → ((𝜑𝜒) ↔ (𝜓𝜒)))
21notbid 310 . 2 ((𝜑𝜓) → (¬ (𝜑𝜒) ↔ ¬ (𝜓𝜒)))
3 df-nan 1610 . 2 ((𝜑𝜒) ↔ ¬ (𝜑𝜒))
4 df-nan 1610 . 2 ((𝜓𝜒) ↔ ¬ (𝜓𝜒))
52, 3, 43bitr4g 306 1 ((𝜑𝜓) → ((𝜑𝜒) ↔ (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)
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