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Theorem annotanannotOLD 1035
Description: Obsolete proof of annotanannot 864 as of 1-Apr-2022. (Contributed by AV, 8-Mar-2022.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
annotanannotOLD ((𝜑 ∧ ¬ (𝜑𝜓)) ↔ (𝜑 ∧ ¬ 𝜓))

Proof of Theorem annotanannotOLD
StepHypRef Expression
1 ianor 1005 . . 3 (¬ (𝜑𝜓) ↔ (¬ 𝜑 ∨ ¬ 𝜓))
21anbi2i 617 . 2 ((𝜑 ∧ ¬ (𝜑𝜓)) ↔ (𝜑 ∧ (¬ 𝜑 ∨ ¬ 𝜓)))
3 andi 1031 . 2 ((𝜑 ∧ (¬ 𝜑 ∨ ¬ 𝜓)) ↔ ((𝜑 ∧ ¬ 𝜑) ∨ (𝜑 ∧ ¬ 𝜓)))
4 pm3.24 392 . . . . 5 ¬ (𝜑 ∧ ¬ 𝜑)
54pm2.21i 117 . . . 4 ((𝜑 ∧ ¬ 𝜑) → (𝜑 ∧ ¬ 𝜓))
6 id 22 . . . 4 ((𝜑 ∧ ¬ 𝜓) → (𝜑 ∧ ¬ 𝜓))
75, 6jaoi 884 . . 3 (((𝜑 ∧ ¬ 𝜑) ∨ (𝜑 ∧ ¬ 𝜓)) → (𝜑 ∧ ¬ 𝜓))
8 olc 895 . . 3 ((𝜑 ∧ ¬ 𝜓) → ((𝜑 ∧ ¬ 𝜑) ∨ (𝜑 ∧ ¬ 𝜓)))
97, 8impbii 201 . 2 (((𝜑 ∧ ¬ 𝜑) ∨ (𝜑 ∧ ¬ 𝜓)) ↔ (𝜑 ∧ ¬ 𝜓))
102, 3, 93bitri 289 1 ((𝜑 ∧ ¬ (𝜑𝜓)) ↔ (𝜑 ∧ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 198  wa 385  wo 874
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-or 875
This theorem is referenced by: (None)
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