Theorem imp44 429

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 424	. 2 ⊢ (𝜑 → (((𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜏))
3	2	imp 407	1 ⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜏)

Syntax hints:   → wi 4   ∧ wa 396

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 397

This theorem is referenced by:  imp511  444  rnelfm  23104  mdsymlem4  30768  mdsymlem5  30769  cvrat4  37457