Theorem biimtrdi

Description: A mixed syllogism inference. (Contributed by NM, 2-Jan-1994)

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

Proof

Step	Hyp	Ref	Expression
1		biimtrdi.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2		biimtrdi.2	⊢ ( 𝜒 → 𝜃 )
3	1	biimpd	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4	3 2	syl6	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )