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Theorem confun2 39756
Description: Confun simplified to two propositions. (Contributed by Jarvin Udandy, 6-Sep-2020.)
Hypotheses
Ref Expression
confun2.1 (𝜓𝜑)
confun2.2 (𝜓 → ¬ (𝜓 → (𝜓 ∧ ¬ 𝜓)))
confun2.3 ((𝜓𝜑) → ((𝜓𝜑) → 𝜑))
Assertion
Ref Expression
confun2 (𝜓 → (¬ (𝜓 → (𝜓 ∧ ¬ 𝜓)) ↔ (𝜓𝜑)))

Proof of Theorem confun2
StepHypRef Expression
1 confun2.1 . 2 (𝜓𝜑)
2 confun2.2 . 2 (𝜓 → ¬ (𝜓 → (𝜓 ∧ ¬ 𝜓)))
3 confun2.3 . 2 ((𝜓𝜑) → ((𝜓𝜑) → 𝜑))
41, 1, 2, 3confun 39755 1 (𝜓 → (¬ (𝜓 → (𝜓 ∧ ¬ 𝜓)) ↔ (𝜓𝜑)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 195  wa 383
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 196
This theorem is referenced by: (None)
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