Theorem sylan2b

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

	Ref	Expression
Hypotheses	sylan2b.1	⊢ ( 𝜑 ↔ 𝜒 )
	sylan2b.2	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	sylan2b	⊢ ( ( 𝜓 ∧ 𝜑 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		sylan2b.1	⊢ ( 𝜑 ↔ 𝜒 )
2		sylan2b.2	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
3	1	biimpi	⊢ ( 𝜑 → 𝜒 )
4	3 2	sylan2	⊢ ( ( 𝜓 ∧ 𝜑 ) → 𝜃 )