Theorem bj-imim21

Description: The propositional function ( ch -> ( . -> th ) ) is decreasing. (Contributed by BJ, 19-Jul-2019)

	Ref	Expression
Assertion	bj-imim21	$$⊢\left(\phi \to \psi \right)\to \left(\left(\chi \to \left(\psi \to \theta \right)\right)\to \left(\chi \to \left(\phi \to \theta \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		imim1	$$⊢\left(\phi \to \psi \right)\to \left(\left(\psi \to \theta \right)\to \left(\phi \to \theta \right)\right)$$
2	1	imim2d	$$⊢\left(\phi \to \psi \right)\to \left(\left(\chi \to \left(\psi \to \theta \right)\right)\to \left(\chi \to \left(\phi \to \theta \right)\right)\right)$$