Theorem embantd

Description: Deduction embedding an antecedent. (Contributed by Wolf Lammen, 4-Oct-2013)

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

Proof

Step	Hyp	Ref	Expression
1		embantd.1	$$⊢\phi \to \psi$$
2		embantd.2	$$⊢\phi \to \left(\chi \to \theta \right)$$
3	2	imim2d	$$⊢\phi \to \left(\left(\psi \to \chi \right)\to \left(\psi \to \theta \right)\right)$$
4	1 3	mpid	$$⊢\phi \to \left(\left(\psi \to \chi \right)\to \theta \right)$$