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Metamath Proof Explorer

Theorem mpbirand

Description: Detach truth from conjunction in biconditional. (Contributed by Glauco Siliprandi, 3-Mar-2021)

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

Proof

Step Hyp Ref Expression
1 mpbirand.1 ⊢ φ → χ
2 mpbirand.2 ⊢ φ → ψ ↔ χ ∧ θ
3 1 biantrurd ⊢ φ → θ ↔ χ ∧ θ
4 2 3 bitr4d ⊢ φ → ψ ↔ θ