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Theorem clifte 40393
Description: show d is the same as an if-else involving a,b. (Contributed by Jarvin Udandy, 20-Sep-2020.)
Hypotheses
Ref Expression
clifte.1 (𝜑 ∧ ¬ 𝜒)
clifte.2 𝜃
Assertion
Ref Expression
clifte (𝜃 ↔ ((𝜑 ∧ ¬ 𝜒) ∨ (𝜓𝜒)))

Proof of Theorem clifte
StepHypRef Expression
1 clifte.2 . 2 𝜃
2 clifte.1 . . 3 (𝜑 ∧ ¬ 𝜒)
32orci 405 . 2 ((𝜑 ∧ ¬ 𝜒) ∨ (𝜓𝜒))
41, 32th 254 1 (𝜃 ↔ ((𝜑 ∧ ¬ 𝜒) ∨ (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wo 383  wa 384
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 197  df-or 385
This theorem is referenced by: (None)
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