Theorem syl6

Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. (Contributed by NM, 5-Jan-1993) (Proof shortened by Wolf Lammen, 30-Jul-2012)

	Ref	Expression
Hypotheses	syl6.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	syl6.2	$$⊢\chi \to \theta$$
Assertion	syl6	$$⊢\phi \to \left(\psi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		syl6.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		syl6.2	$$⊢\chi \to \theta$$
3	2	a1i	$$⊢\psi \to \left(\chi \to \theta \right)$$
4	1 3	sylcom	$$⊢\phi \to \left(\psi \to \theta \right)$$