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Theorem cliftetb 39754
Description: show d is the same as an if-else involving a,b. (Contributed by Jarvin Udandy, 20-Sep-2020.)
Hypotheses
Ref Expression
cliftetb.1 ((𝜑𝜒) ∨ (𝜓 ∧ ¬ 𝜒))
cliftetb.2 𝜃
Assertion
Ref Expression
cliftetb (𝜃 ↔ ((𝜑𝜒) ∨ (𝜓 ∧ ¬ 𝜒)))

Proof of Theorem cliftetb
StepHypRef Expression
1 cliftetb.2 . 2 𝜃
2 cliftetb.1 . 2 ((𝜑𝜒) ∨ (𝜓 ∧ ¬ 𝜒))
31, 22th 253 1 (𝜃 ↔ ((𝜑𝜒) ∨ (𝜓 ∧ ¬ 𝜒)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 195  wo 382  wa 383
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
This theorem is referenced by: (None)
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