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Theorem ifpdfor2 36824
Description: Define or in terms of conditional logic operator. (Contributed by RP, 20-Apr-2020.)
Assertion
Ref Expression
ifpdfor2 ((𝜑𝜓) ↔ if-(𝜑, 𝜑, 𝜓))

Proof of Theorem ifpdfor2
StepHypRef Expression
1 pm2.1 432 . . 3 𝜑𝜑)
21biantrur 526 . 2 ((𝜑𝜓) ↔ ((¬ 𝜑𝜑) ∧ (𝜑𝜓)))
3 dfifp4 1010 . 2 (if-(𝜑, 𝜑, 𝜓) ↔ ((¬ 𝜑𝜑) ∧ (𝜑𝜓)))
42, 3bitr4i 266 1 ((𝜑𝜓) ↔ if-(𝜑, 𝜑, 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 195  wo 382  wa 383  if-wif 1006
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  df-or 384  df-an 385  df-ifp 1007
This theorem is referenced by:  ifporcor  36825
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