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Metamath Proof Explorer

Theorem pm4.71d

Description: Deduction converting an implication to a biconditional with conjunction. Deduction from Theorem *4.71 of WhiteheadRussell p. 120. (Contributed by Mario Carneiro, 25-Dec-2016)

Ref Expression
Hypothesis pm4.71rd.1 ⊢ φ → ψ → χ
Assertion pm4.71d ⊢ φ → ψ ↔ ψ ∧ χ

Proof

Step Hyp Ref Expression
1 pm4.71rd.1 ⊢ φ → ψ → χ
2 pm4.71 ⊢ ψ → χ ↔ ψ ↔ ψ ∧ χ
3 1 2 sylib ⊢ φ → ψ ↔ ψ ∧ χ