Theorem bj-imim21i

Description: Inference associated with bj-imim21 . Its associated inference is syl5 . (Contributed by BJ, 19-Jul-2019)

	Ref	Expression
Hypothesis	bj-imim21i.1	$$⊢\phi \to \psi$$
Assertion	bj-imim21i	$$⊢\left(\chi \to \left(\psi \to \theta \right)\right)\to \left(\chi \to \left(\phi \to \theta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		bj-imim21i.1	$$⊢\phi \to \psi$$
2		bj-imim21	$$⊢\left(\phi \to \psi \right)\to \left(\left(\chi \to \left(\psi \to \theta \right)\right)\to \left(\chi \to \left(\phi \to \theta \right)\right)\right)$$
3	1 2	ax-mp	$$⊢\left(\chi \to \left(\psi \to \theta \right)\right)\to \left(\chi \to \left(\phi \to \theta \right)\right)$$