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Metamath Proof Explorer

Theorem bitr3d

Description: Deduction form of bitr3i . (Contributed by NM, 14-May-1993)

Ref Expression
Hypotheses bitr3d.1 ⊢ φ → ψ ↔ χ
bitr3d.2 ⊢ φ → ψ ↔ θ
Assertion bitr3d ⊢ φ → χ ↔ θ

Proof

Step Hyp Ref Expression
1 bitr3d.1 ⊢ φ → ψ ↔ χ
2 bitr3d.2 ⊢ φ → ψ ↔ θ
3 1 bicomd ⊢ φ → χ ↔ ψ
4 3 2 bitrd ⊢ φ → χ ↔ θ