Theorem 3syl

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

	Ref	Expression
Hypotheses	3syl.1	$$⊢\phi \to \psi$$
	3syl.2	$$⊢\psi \to \chi$$
	3syl.3	$$⊢\chi \to \theta$$
Assertion	3syl	$$⊢\phi \to \theta$$

Proof

Step	Hyp	Ref	Expression
1		3syl.1	$$⊢\phi \to \psi$$
2		3syl.2	$$⊢\psi \to \chi$$
3		3syl.3	$$⊢\chi \to \theta$$
4	1 2	syl	$$⊢\phi \to \chi$$
5	4 3	syl	$$⊢\phi \to \theta$$