Theorem syl2imc

Description: A commuted version of syl2im . Implication-only version of syl2anr . (Contributed by BJ, 20-Oct-2021)

	Ref	Expression
Hypotheses	syl2im.1	$$⊢\phi \to \psi$$
	syl2im.2	$$⊢\chi \to \theta$$
	syl2im.3	$$⊢\psi \to \left(\theta \to \tau \right)$$
Assertion	syl2imc	$$⊢\chi \to \left(\phi \to \tau \right)$$

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	1 2 3	syl2im	$$⊢\phi \to \left(\chi \to \tau \right)$$
5	4	com12	$$⊢\chi \to \left(\phi \to \tau \right)$$