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Metamath Proof Explorer

Theorem 3bitrd

Description: Deduction from transitivity of biconditional. (Contributed by NM, 13-Aug-1999)

Ref Expression
Hypotheses 3bitrd.1 ⊢ φ → ψ ↔ χ
3bitrd.2 ⊢ φ → χ ↔ θ
3bitrd.3 ⊢ φ → θ ↔ τ
Assertion 3bitrd ⊢ φ → ψ ↔ τ

Proof

Step Hyp Ref Expression
1 3bitrd.1 ⊢ φ → ψ ↔ χ
2 3bitrd.2 ⊢ φ → χ ↔ θ
3 3bitrd.3 ⊢ φ → θ ↔ τ
4 1 2 bitrd ⊢ φ → ψ ↔ θ
5 4 3 bitrd ⊢ φ → ψ ↔ τ