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	⊢ ( 𝜑 → 𝜓 )
Assertion	bj-imim11i	⊢ ( ( ( 𝜑 → 𝜒 ) → 𝜃 ) → ( ( 𝜓 → 𝜒 ) → 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		bj-imim11i.1	⊢ ( 𝜑 → 𝜓 )
2		bj-imim11	⊢ ( ( 𝜑 → 𝜓 ) → ( ( ( 𝜑 → 𝜒 ) → 𝜃 ) → ( ( 𝜓 → 𝜒 ) → 𝜃 ) ) )
3	1 2	ax-mp	⊢ ( ( ( 𝜑 → 𝜒 ) → 𝜃 ) → ( ( 𝜓 → 𝜒 ) → 𝜃 ) )