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Metamath Proof Explorer

Theorem pm5.74i

Description: Distribution of implication over biconditional (inference form). (Contributed by NM, 1-Aug-1994)

Ref Expression
Hypothesis pm5.74i.1 ⊢ φ → ψ ↔ χ
Assertion pm5.74i ⊢ φ → ψ ↔ φ → χ

Proof

Step Hyp Ref Expression
1 pm5.74i.1 ⊢ φ → ψ ↔ χ
2 pm5.74 ⊢ φ → ψ ↔ χ ↔ φ → ψ ↔ φ → χ
3 1 2 mpbi ⊢ φ → ψ ↔ φ → χ