Theorem syl2im

Description: Replace two antecedents. Implication-only version of syl2an . (Contributed by Wolf Lammen, 14-May-2013)

	Ref	Expression
Hypotheses	syl2im.1	$$⊢\phi \to \psi$$
	syl2im.2	$$⊢\chi \to \theta$$
	syl2im.3	$$⊢\psi \to \left(\theta \to \tau \right)$$
Assertion	syl2im	$$⊢\phi \to \left(\chi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		syl2im.1	$$⊢\phi \to \psi$$
2		syl2im.2	$$⊢\chi \to \theta$$
3		syl2im.3	$$⊢\psi \to \left(\theta \to \tau \right)$$
4	2 3	syl5	$$⊢\psi \to \left(\chi \to \tau \right)$$
5	1 4	syl	$$⊢\phi \to \left(\chi \to \tau \right)$$