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Theorem bigolden 899
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 pm4.71 381 . 2 ((𝜑𝜓) ↔ (𝜑 ↔ (𝜑𝜓)))
2 pm4.72 770 . 2 ((𝜑𝜓) ↔ (𝜓 ↔ (𝜑𝜓)))
3 bicom 138 . 2 ((𝜑 ↔ (𝜑𝜓)) ↔ ((𝜑𝜓) ↔ 𝜑))
41, 2, 33bitr3ri 209 1 (((𝜑𝜓) ↔ 𝜑) ↔ (𝜓 ↔ (𝜑𝜓)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wb 103  wo 662
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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