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Theorem bigolden 901
Description: Dijkstra-Scholten's Golden Rule for calculational proofs. (Contributed by NM, 10-Jan-2005.)
Assertion
Ref Expression
bigolden (((φ ψ) ↔ φ) ↔ (ψ ↔ (φ ψ)))

Proof of Theorem bigolden
StepHypRef Expression
1 pm4.71 611 . 2 ((φψ) ↔ (φ ↔ (φ ψ)))
2 pm4.72 846 . 2 ((φψ) ↔ (ψ ↔ (φ ψ)))
3 bicom 191 . 2 ((φ ↔ (φ ψ)) ↔ ((φ ψ) ↔ φ))
41, 2, 33bitr3ri 267 1 (((φ ψ) ↔ φ) ↔ (ψ ↔ (φ ψ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wo 357   wa 358
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 177  df-or 359  df-an 360
This theorem is referenced by: (None)
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