Theorem wl-syls2

Description: Replacing a nested antecedent. A sort of syllogism in antecedent position. (Contributed by Wolf Lammen, 20-Sep-2013) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	wl-syls2.1	$$⊢\phi \to \psi$$
	wl-syls2.2	$$⊢\left(\phi \to \chi \right)\to \theta$$
Assertion	wl-syls2	$$⊢\left(\psi \to \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		wl-syls2.1	$$⊢\phi \to \psi$$
2		wl-syls2.2	$$⊢\left(\phi \to \chi \right)\to \theta$$
3	1	imim1i	$$⊢\left(\psi \to \chi \right)\to \left(\phi \to \chi \right)$$
4	3 2	syl	$$⊢\left(\psi \to \chi \right)\to \theta$$