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Metamath Proof Explorer

Theorem biadani

Description: Inference associated with biadan . (Contributed by BJ, 4-Mar-2023)

Ref Expression
Hypothesis biadani.1 ⊢ φ → ψ
Assertion biadani ⊢ ψ → φ ↔ χ ↔ φ ↔ ψ ∧ χ

Proof

Step Hyp Ref Expression
1 biadani.1 ⊢ φ → ψ
2 biadan ⊢ φ → ψ ↔ ψ → φ ↔ χ ↔ φ ↔ ψ ∧ χ
3 1 2 mpbi ⊢ ψ → φ ↔ χ ↔ φ ↔ ψ ∧ χ