Theorem bitr2d

Description: Deduction form of bitr2i . (Contributed by NM, 9-Jun-2004)

	Ref	Expression
Hypotheses	bitr2d.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
	bitr2d.2	⊢ ( 𝜑 → ( 𝜒 ↔ 𝜃 ) )
Assertion	bitr2d	⊢ ( 𝜑 → ( 𝜃 ↔ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		bitr2d.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2		bitr2d.2	⊢ ( 𝜑 → ( 𝜒 ↔ 𝜃 ) )
3	1 2	bitrd	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜃 ) )
4	3	bicomd	⊢ ( 𝜑 → ( 𝜃 ↔ 𝜓 ) )