Theorem bj-imim11i

Description: The propositional function ( ( . -> ph ) -> ps ) is increasing. Its associated inference is wl-syls2 . (Contributed by BJ, 3-Apr-2026)

	Ref	Expression
Hypothesis	bj-imim11i.1	$$⊢\phi \to \psi$$
Assertion	bj-imim11i	$$⊢\left(\left(\phi \to \chi \right)\to \theta \right)\to \left(\left(\psi \to \chi \right)\to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		bj-imim11i.1	$$⊢\phi \to \psi$$
2		bj-imim11	$$⊢\left(\phi \to \psi \right)\to \left(\left(\left(\phi \to \chi \right)\to \theta \right)\to \left(\left(\psi \to \chi \right)\to \theta \right)\right)$$
3	1 2	ax-mp	$$⊢\left(\left(\phi \to \chi \right)\to \theta \right)\to \left(\left(\psi \to \chi \right)\to \theta \right)$$