Theorem mpsyl

Description: Modus ponens combined with a syllogism inference. (Contributed by Alan Sare, 20-Apr-2011)

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

Proof

Step	Hyp	Ref	Expression
1		mpsyl.1	$$⊢\phi$$
2		mpsyl.2	$$⊢\psi \to \chi$$
3		mpsyl.3	$$⊢\phi \to \left(\chi \to \theta \right)$$
4	1	a1i	$$⊢\psi \to \phi$$
5	4 2 3	sylc	$$⊢\psi \to \theta$$