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Theorem clifteta 43050
Description: show d is the same as an if-else involving a,b. (Contributed by Jarvin Udandy, 20-Sep-2020.)
Hypotheses
Ref Expression
clifteta.1 ((𝜑 ∧ ¬ 𝜒) ∨ (𝜓𝜒))
clifteta.2 𝜃
Assertion
Ref Expression
clifteta (𝜃 ↔ ((𝜑 ∧ ¬ 𝜒) ∨ (𝜓𝜒)))

Proof of Theorem clifteta
StepHypRef Expression
1 clifteta.2 . 2 𝜃
2 clifteta.1 . 2 ((𝜑 ∧ ¬ 𝜒) ∨ (𝜓𝜒))
31, 22th 265 1 (𝜃 ↔ ((𝜑 ∧ ¬ 𝜒) ∨ (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  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
This theorem is referenced by: (None)
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