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Metamath Proof Explorer

Theorem impbid21d

Description: Deduce an equivalence from two implications. (Contributed by Wolf Lammen, 12-May-2013)

Ref Expression
Hypotheses impbid21d.1 ⊢ ψ → χ → θ
impbid21d.2 ⊢ φ → θ → χ
Assertion impbid21d ⊢ φ → ψ → χ ↔ θ

Proof

Step Hyp Ref Expression
1 impbid21d.1 ⊢ ψ → χ → θ
2 impbid21d.2 ⊢ φ → θ → χ
3 impbi ⊢ χ → θ → θ → χ → χ ↔ θ
4 1 2 3 syl2imc ⊢ φ → ψ → χ ↔ θ