Theorem bj-imim11i 37341

Description: The propositional function ((. → 𝜑) → 𝜓) is increasing. Its associated inference is wl-syls2 38361. (Contributed by BJ, 3-Apr-2026.)

Hypothesis

Ref	Expression
bj-imim11i.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
bj-imim11i	⊢ (((𝜑 → 𝜒) → 𝜃) → ((𝜓 → 𝜒) → 𝜃))

Proof of Theorem bj-imim11i

Step	Hyp	Ref	Expression
1		bj-imim11i.1	. 2 ⊢ (𝜑 → 𝜓)
2		bj-imim11 37340	. 2 ⊢ ((𝜑 → 𝜓) → (((𝜑 → 𝜒) → 𝜃) → ((𝜓 → 𝜒) → 𝜃)))
3	1, 2	ax-mp 5	1 ⊢ (((𝜑 → 𝜒) → 𝜃) → ((𝜓 → 𝜒) → 𝜃))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by: (None)