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Metamath Proof Explorer

Theorem impexp

Description: Import-export theorem. Part of Theorem *4.87 of WhiteheadRussell p. 122. (Contributed by NM, 10-Jan-1993) (Proof shortened by Wolf Lammen, 24-Mar-2013)

Ref Expression
Assertion impexp ⊢ φ ∧ ψ → χ ↔ φ → ψ → χ

Proof

Step Hyp Ref Expression
1 pm3.3 ⊢ φ ∧ ψ → χ → φ → ψ → χ
2 pm3.31 ⊢ φ → ψ → χ → φ ∧ ψ → χ
3 1 2 impbii ⊢ φ ∧ ψ → χ ↔ φ → ψ → χ