Theorem sylan2br

Description: A syllogism inference. (Contributed by NM, 21-Apr-1994)

	Ref	Expression
Hypotheses	sylan2br.1	⊢ ( 𝜒 ↔ 𝜑 )
	sylan2br.2	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	sylan2br	⊢ ( ( 𝜓 ∧ 𝜑 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		sylan2br.1	⊢ ( 𝜒 ↔ 𝜑 )
2		sylan2br.2	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
3	1	biimpri	⊢ ( 𝜑 → 𝜒 )
4	3 2	sylan2	⊢ ( ( 𝜓 ∧ 𝜑 ) → 𝜃 )