Theorem imim3i 55

Description: Inference adding three nested antecedents. (Contributed by NM, 19-Dec-2006.)

Hypothesis

Ref	Expression
imim3i.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
imim3i	⊢ ((𝜃 → 𝜑) → ((𝜃 → 𝜓) → (𝜃 → 𝜒)))

Proof of Theorem imim3i

Step	Hyp	Ref	Expression
1		imim3i.1	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
2	1	imim2i 12	. 2 ⊢ ((𝜃 → 𝜑) → (𝜃 → (𝜓 → 𝜒)))
3	2	a2d 23	1 ⊢ ((𝜃 → 𝜑) → ((𝜃 → 𝜓) → (𝜃 → 𝜒)))

Syntax hints:   → wi 4

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

This theorem is referenced by:  pm2.83  71  pm5.74  168  bi3ant  213  pm3.43i  258  ceqsalt  2580