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Theorem nancomOLD 1615
 Description: Obsolete proof of nancom 1614 as of 19-Oct-2022. (Contributed by Mario Carneiro, 9-May-2015.) (Proof shortened by Wolf Lammen, 7-Mar-2020.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nancomOLD ((𝜑𝜓) ↔ (𝜓𝜑))

Proof of Theorem nancomOLD
StepHypRef Expression
1 df-nan 1610 . . 3 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
2 ancom 453 . . 3 ((𝜑𝜓) ↔ (𝜓𝜑))
31, 2xchbinx 326 . 2 ((𝜑𝜓) ↔ ¬ (𝜓𝜑))
4 df-nan 1610 . 2 ((𝜓𝜑) ↔ ¬ (𝜓𝜑))
53, 4bitr4i 270 1 ((𝜑𝜓) ↔ (𝜓𝜑))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ↔ 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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