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Metamath Proof Explorer

Theorem impbid2

Description: Infer an equivalence from two implications. (Contributed by NM, 6-Mar-2007) (Proof shortened by Wolf Lammen, 27-Sep-2013)

Ref Expression
Hypotheses impbid2.1 ⊢ ψ → χ
impbid2.2 ⊢ φ → χ → ψ
Assertion impbid2 ⊢ φ → ψ ↔ χ

Proof

Step Hyp Ref Expression
1 impbid2.1 ⊢ ψ → χ
2 impbid2.2 ⊢ φ → χ → ψ
3 2 1 impbid1 ⊢ φ → χ ↔ ψ
4 3 bicomd ⊢ φ → ψ ↔ χ