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Theorem bigolden 861
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 pm4.71 369 . 2 ((φψ) ↔ (φ ↔ (φ ψ)))
2 pm4.72 735 . 2 ((φψ) ↔ (ψ ↔ (φ ψ)))
3 bicom 128 . 2 ((φ ↔ (φ ψ)) ↔ ((φ ψ) ↔ φ))
41, 2, 33bitr3ri 200 1 (((φ ψ) ↔ φ) ↔ (ψ ↔ (φ ψ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98   wo 628
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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