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Theorem rb-bijust 1664
Description: Justification for rb-imdf 1665. (Contributed by Anthony Hart, 17-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
rb-bijust ((𝜑𝜓) ↔ ¬ (¬ (¬ 𝜑𝜓) ∨ ¬ (¬ 𝜓𝜑)))

Proof of Theorem rb-bijust
StepHypRef Expression
1 dfbi1 201 . 2 ((𝜑𝜓) ↔ ¬ ((𝜑𝜓) → ¬ (𝜓𝜑)))
2 imor 426 . . . 4 ((𝜑𝜓) ↔ (¬ 𝜑𝜓))
3 imor 426 . . . . 5 ((𝜓𝜑) ↔ (¬ 𝜓𝜑))
43notbii 308 . . . 4 (¬ (𝜓𝜑) ↔ ¬ (¬ 𝜓𝜑))
52, 4imbi12i 338 . . 3 (((𝜑𝜓) → ¬ (𝜓𝜑)) ↔ ((¬ 𝜑𝜓) → ¬ (¬ 𝜓𝜑)))
65notbii 308 . 2 (¬ ((𝜑𝜓) → ¬ (𝜓𝜑)) ↔ ¬ ((¬ 𝜑𝜓) → ¬ (¬ 𝜓𝜑)))
7 pm4.62 433 . . 3 (((¬ 𝜑𝜓) → ¬ (¬ 𝜓𝜑)) ↔ (¬ (¬ 𝜑𝜓) ∨ ¬ (¬ 𝜓𝜑)))
87notbii 308 . 2 (¬ ((¬ 𝜑𝜓) → ¬ (¬ 𝜓𝜑)) ↔ ¬ (¬ (¬ 𝜑𝜓) ∨ ¬ (¬ 𝜓𝜑)))
91, 6, 83bitri 284 1 ((𝜑𝜓) ↔ ¬ (¬ (¬ 𝜑𝜓) ∨ ¬ (¬ 𝜓𝜑)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 194  wo 381
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 195  df-or 383
This theorem is referenced by:  rb-imdf  1665
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