Theorem syl6bbr

Description: A syllogism inference from two biconditionals. (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Hypotheses	syl6bbr.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
	syl6bbr.2	⊢ ( 𝜃 ↔ 𝜒 )
Assertion	syl6bbr	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		syl6bbr.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2		syl6bbr.2	⊢ ( 𝜃 ↔ 𝜒 )
3	2	bicomi	⊢ ( 𝜒 ↔ 𝜃 )
4	1 3	syl6bb	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜃 ) )