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Metamath Proof Explorer

Theorem pm5.21nii

Description: Eliminate an antecedent implied by each side of a biconditional. (Contributed by NM, 21-May-1999)

Ref Expression
Hypotheses pm5.21ni.1 ⊢ φ → ψ
pm5.21ni.2 ⊢ χ → ψ
pm5.21nii.3 ⊢ ψ → φ ↔ χ
Assertion pm5.21nii ⊢ φ ↔ χ

Proof

Step Hyp Ref Expression
1 pm5.21ni.1 ⊢ φ → ψ
2 pm5.21ni.2 ⊢ χ → ψ
3 pm5.21nii.3 ⊢ ψ → φ ↔ χ
4 1 2 pm5.21ni ⊢ ¬ ψ → φ ↔ χ
5 3 4 pm2.61i ⊢ φ ↔ χ