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Theorem biimpor 32836
Description: A rewriting rule for biimplication. (Contributed by Giovanni Mascellani, 15-Sep-2017.)
Assertion
Ref Expression
biimpor (((𝜑𝜓) → 𝜒) ↔ ((¬ 𝜑𝜓) ∨ 𝜒))

Proof of Theorem biimpor
StepHypRef Expression
1 imor 426 . 2 (((𝜑𝜓) → 𝜒) ↔ (¬ (𝜑𝜓) ∨ 𝜒))
2 notbinot2 32835 . . 3 (¬ (𝜑𝜓) ↔ (¬ 𝜑𝜓))
32orbi1i 540 . 2 ((¬ (𝜑𝜓) ∨ 𝜒) ↔ ((¬ 𝜑𝜓) ∨ 𝜒))
41, 3bitri 262 1 (((𝜑𝜓) → 𝜒) ↔ ((¬ 𝜑𝜓) ∨ 𝜒))
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: (None)
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