Theorem bj-imim21 37167

Description: The propositional function (𝜑 → (. → 𝜓)) is decreasing. (Contributed by BJ, 19-Jul-2019.)

Assertion

Ref	Expression
bj-imim21	⊢ ((𝜑 → 𝜓) → ((𝜒 → (𝜓 → 𝜃)) → (𝜒 → (𝜑 → 𝜃))))

Proof of Theorem bj-imim21

Step	Hyp	Ref	Expression
1		imim1 84	. 2 ⊢ ((𝜑 → 𝜓) → ((𝜓 → 𝜃) → (𝜑 → 𝜃)))
2	1	imim2d 58	1 ⊢ ((𝜑 → 𝜓) → ((𝜒 → (𝜓 → 𝜃)) → (𝜒 → (𝜑 → 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:  bj-imim21i  37168  bj-axc4  37217