Users' Mathboxes Mathbox for Jarvin Udandy < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  clifteta Structured version   Visualization version   GIF version

Theorem clifteta 43523
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 267 1 (𝜃 ↔ ((𝜑 ∧ ¬ 𝜒) ∨ (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 209  wa 399  wo 844
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 210
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator