Theorem bj-imim11 36781

Description: The propositional function ((. → 𝜑) → 𝜓) is increasing. (Contributed by BJ, 3-Apr-2026.)

Assertion

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

Proof of Theorem bj-imim11

Step	Hyp	Ref	Expression
1		imim1 83	. 2 ⊢ ((𝜑 → 𝜓) → ((𝜓 → 𝜒) → (𝜑 → 𝜒)))
2	1	imim1d 82	1 ⊢ ((𝜑 → 𝜓) → (((𝜑 → 𝜒) → 𝜃) → ((𝜓 → 𝜒) → 𝜃)))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  bj-imim11i  36782