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Metamath Proof Explorer

Theorem pm5.6

Description: Conjunction in antecedent versus disjunction in consequent. Theorem *5.6 of WhiteheadRussell p. 125. (Contributed by NM, 8-Jun-1994)

Ref Expression
Assertion pm5.6 ⊢ φ ∧ ¬ ψ → χ ↔ φ → ψ ∨ χ

Proof

Step Hyp Ref Expression
1 impexp ⊢ φ ∧ ¬ ψ → χ ↔ φ → ¬ ψ → χ
2 df-or ⊢ ψ ∨ χ ↔ ¬ ψ → χ
3 2 imbi2i ⊢ φ → ψ ∨ χ ↔ φ → ¬ ψ → χ
4 1 3 bitr4i ⊢ φ ∧ ¬ ψ → χ ↔ φ → ψ ∨ χ