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Metamath Proof Explorer

Theorem bitrd

Description: Deduction form of bitri . (Contributed by NM, 12-Mar-1993) (Proof shortened by Wolf Lammen, 14-Apr-2013)

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

Proof

Step Hyp Ref Expression
1 bitrd.1 ⊢ φ → ψ ↔ χ
2 bitrd.2 ⊢ φ → χ ↔ θ
3 1 pm5.74i ⊢ φ → ψ ↔ φ → χ
4 2 pm5.74i ⊢ φ → χ ↔ φ → θ
5 3 4 bitri ⊢ φ → ψ ↔ φ → θ
6 5 pm5.74ri ⊢ φ → ψ ↔ θ