Theorem bitr4d

Description: Deduction form of bitr4i . (Contributed by NM, 30-Jun-1993)

	Ref	Expression
Hypotheses	bitr4d.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
	bitr4d.2	⊢ ( 𝜑 → ( 𝜃 ↔ 𝜒 ) )
Assertion	bitr4d	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		bitr4d.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2		bitr4d.2	⊢ ( 𝜑 → ( 𝜃 ↔ 𝜒 ) )
3	2	bicomd	⊢ ( 𝜑 → ( 𝜒 ↔ 𝜃 ) )
4	1 3	bitrd	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜃 ) )