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 ) )