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Theorem dfifp4 1067
Description: Alternate definition of the conditional operator for propositions. (Contributed by BJ, 30-Sep-2019.)
Assertion
Ref Expression
dfifp4 (if-(𝜑, 𝜓, 𝜒) ↔ ((¬ 𝜑𝜓) ∧ (𝜑𝜒)))

Proof of Theorem dfifp4
StepHypRef Expression
1 dfifp3 1066 . 2 (if-(𝜑, 𝜓, 𝜒) ↔ ((𝜑𝜓) ∧ (𝜑𝜒)))
2 imor 854 . 2 ((𝜑𝜓) ↔ (¬ 𝜑𝜓))
31, 2bianbi 627 1 (if-(𝜑, 𝜓, 𝜒) ↔ ((¬ 𝜑𝜓) ∧ (𝜑𝜒)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 206  wa 395  wo 848  if-wif 1063
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 207  df-an 396  df-or 849  df-ifp 1064
This theorem is referenced by:  anifp  1072  ifpan123g  43472  ifpan23  43473  ifpdfor2  43474  ifpdfor  43478  ifpim1  43482  ifpnot  43483  ifpid2  43484  ifpim2  43485  ifpnot23  43491  ifpidg  43504  ifpim123g  43513  ifpimim  43522
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