Theorem bj-imim21i 37168

Description: The propositional function (𝜑 → (. → 𝜓)) is decreasing. Its associated inference is syl5 35. (Contributed by BJ, 19-Jul-2019.)

Hypothesis

Ref	Expression
bj-imim21i.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
bj-imim21i	⊢ ((𝜒 → (𝜓 → 𝜃)) → (𝜒 → (𝜑 → 𝜃)))

Proof of Theorem bj-imim21i

Step	Hyp	Ref	Expression
1		bj-imim21i.1	. 2 ⊢ (𝜑 → 𝜓)
2		bj-imim21 37167	. 2 ⊢ ((𝜑 → 𝜓) → ((𝜒 → (𝜓 → 𝜃)) → (𝜒 → (𝜑 → 𝜃))))
3	1, 2	ax-mp 5	1 ⊢ ((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: (None)