Theorem syl8

Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. (Contributed by NM, 1-Aug-1994) (Proof shortened by Wolf Lammen, 3-Aug-2012)

	Ref	Expression
Hypotheses	syl8.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
	syl8.2	$$⊢\theta \to \tau$$
Assertion	syl8	$$⊢\phi \to \left(\psi \to \left(\chi \to \tau \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		syl8.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
2		syl8.2	$$⊢\theta \to \tau$$
3	2	a1i	$$⊢\phi \to \left(\theta \to \tau \right)$$
4	1 3	syl6d	$$⊢\phi \to \left(\psi \to \left(\chi \to \tau \right)\right)$$