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Metamath Proof Explorer

Theorem bigolden

Description: Dijkstra-Scholten's Golden Rule for calculational proofs. (Contributed by NM, 10-Jan-2005)

Ref Expression
Assertion bigolden ⊢ φ ∧ ψ ↔ φ ↔ ψ ↔ φ ∨ ψ

Proof

Step Hyp Ref Expression
1 pm4.71 ⊢ φ → ψ ↔ φ ↔ φ ∧ ψ
2 pm4.72 ⊢ φ → ψ ↔ ψ ↔ φ ∨ ψ
3 bicom ⊢ φ ↔ φ ∧ ψ ↔ φ ∧ ψ ↔ φ
4 1 2 3 3bitr3ri ⊢ φ ∧ ψ ↔ φ ↔ ψ ↔ φ ∨ ψ