Theorem imp4d 430

Description: An importation inference. (Contributed by NM, 26-Apr-1994.)

Hypothesis

Ref	Expression
imp4.1	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Assertion

Ref	Expression
imp4d	⊢ (𝜑 → ((𝜓 ∧ (𝜒 ∧ 𝜃)) → 𝜏))

Proof of Theorem imp4d

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))
2	1	imp4a 428	. 2 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏)))
3	2	impd 416	1 ⊢ (𝜑 → ((𝜓 ∧ (𝜒 ∧ 𝜃)) → 𝜏))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  imp45  435  tfrlem9  8374  uzind  12700  facdiv  14337  cvrexchlem  40226  rexlimdv3d  43447