Theorem 3syl

Description: Inference chaining two syllogisms syl . Inference associated with imim12i . (Contributed by NM, 28-Dec-1992)

	Ref	Expression
Hypotheses	3syl.1	⊢ ( 𝜑 → 𝜓 )
	3syl.2	⊢ ( 𝜓 → 𝜒 )
	3syl.3	⊢ ( 𝜒 → 𝜃 )
Assertion	3syl	⊢ ( 𝜑 → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		3syl.1	⊢ ( 𝜑 → 𝜓 )
2		3syl.2	⊢ ( 𝜓 → 𝜒 )
3		3syl.3	⊢ ( 𝜒 → 𝜃 )
4	1 2	syl	⊢ ( 𝜑 → 𝜒 )
5	4 3	syl	⊢ ( 𝜑 → 𝜃 )