Theorem wl-mps

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

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

Proof

Step	Hyp	Ref	Expression
1		wl-mps.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		wl-mps.2	$$⊢\left(\phi \to \chi \right)\to \theta$$
3	1	a2i	$$⊢\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)$$
4	3 2	syl	$$⊢\left(\phi \to \psi \right)\to \theta$$