Theorem bj-imim11

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

	Ref	Expression
Assertion	bj-imim11	⊢ ( ( 𝜑 → 𝜓 ) → ( ( ( 𝜑 → 𝜒 ) → 𝜃 ) → ( ( 𝜓 → 𝜒 ) → 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		imim1	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜓 → 𝜒 ) → ( 𝜑 → 𝜒 ) ) )
2	1	imim1d	⊢ ( ( 𝜑 → 𝜓 ) → ( ( ( 𝜑 → 𝜒 ) → 𝜃 ) → ( ( 𝜓 → 𝜒 ) → 𝜃 ) ) )