Theorem syl56

Description: Combine syl5 and syl6 . (Contributed by NM, 14-Nov-2013)

	Ref	Expression
Hypotheses	syl56.1	$$⊢\phi \to \psi$$
	syl56.2	$$⊢\chi \to \left(\psi \to \theta \right)$$
	syl56.3	$$⊢\theta \to \tau$$
Assertion	syl56	$$⊢\chi \to \left(\phi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		syl56.1	$$⊢\phi \to \psi$$
2		syl56.2	$$⊢\chi \to \left(\psi \to \theta \right)$$
3		syl56.3	$$⊢\theta \to \tau$$
4	2 3	syl6	$$⊢\chi \to \left(\psi \to \tau \right)$$
5	1 4	syl5	$$⊢\chi \to \left(\phi \to \tau \right)$$