MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  bigolden Structured version   Visualization version   GIF version

Theorem bigolden 975
Description: Dijkstra-Scholten's Golden Rule for calculational proofs. (Contributed by NM, 10-Jan-2005.)
Assertion
Ref Expression
bigolden (((𝜑𝜓) ↔ 𝜑) ↔ (𝜓 ↔ (𝜑𝜓)))

Proof of Theorem bigolden
StepHypRef Expression
1 pm4.71 661 . 2 ((𝜑𝜓) ↔ (𝜑 ↔ (𝜑𝜓)))
2 pm4.72 919 . 2 ((𝜑𝜓) ↔ (𝜓 ↔ (𝜑𝜓)))
3 bicom 212 . 2 ((𝜑 ↔ (𝜑𝜓)) ↔ ((𝜑𝜓) ↔ 𝜑))
41, 2, 33bitr3ri 291 1 (((𝜑𝜓) ↔ 𝜑) ↔ (𝜓 ↔ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  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  df-an 386
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator