Theorem imp44 433

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

Hypothesis

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

Assertion

Ref	Expression
imp44	⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜏)

Proof of Theorem imp44

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))
2	1	imp4c 428	. 2 ⊢ (𝜑 → (((𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜏))
3	2	imp 411	1 ⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜏)

This proof depends on syntax axioms:   → wi 4   ∧ wa 400

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 401

This theorem is used by:  imp511  448  rnelfm  24121  mdsymlem4  32769  mdsymlem5  32770  cvrat4  40245