This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem impbida

Description: Deduce an equivalence from two implications. Variant of impbid . (Contributed by NM, 17-Feb-2007)

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

Proof

Step Hyp Ref Expression
1 impbida.1 ⊢ φ ∧ ψ → χ
2 impbida.2 ⊢ φ ∧ χ → ψ
3 1 ex ⊢ φ → ψ → χ
4 2 ex ⊢ φ → χ → ψ
5 3 4 impbid ⊢ φ → ψ ↔ χ