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Theorem bj-dfbi5 33804
Description: Alternate definition of the biconditional. (Contributed by BJ, 4-Oct-2019.)
Assertion
Ref Expression
bj-dfbi5 ((𝜑𝜓) ↔ ((𝜑𝜓) → (𝜑𝜓)))

Proof of Theorem bj-dfbi5
StepHypRef Expression
1 orcom 864 . 2 (((𝜑𝜓) ∨ ¬ (𝜑𝜓)) ↔ (¬ (𝜑𝜓) ∨ (𝜑𝜓)))
2 bj-dfbi4 33803 . 2 ((𝜑𝜓) ↔ ((𝜑𝜓) ∨ ¬ (𝜑𝜓)))
3 imor 847 . 2 (((𝜑𝜓) → (𝜑𝜓)) ↔ (¬ (𝜑𝜓) ∨ (𝜑𝜓)))
41, 2, 33bitr4i 304 1 ((𝜑𝜓) ↔ ((𝜑𝜓) → (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 207  wa 396  wo 841
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 208  df-an 397  df-or 842
This theorem is referenced by:  bj-dfbi6  33805
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