Theorem imp4c 424

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

Hypothesis

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

Assertion

Ref	Expression
imp4c	⊢ (𝜑 → (((𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜏))

Proof of Theorem imp4c

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))
2	1	impd 411	. 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜃 → 𝜏)))
3	2	impd 411	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:  imp44  429  reuop  6196  omordi  8397  omwordri  8403  omass  8411  oewordri  8423  umgrclwwlkge2  28355  upgr4cycl4dv4e  28549  elspansn5  29936  atcvat3i  30758  mdsymlem5  30769  sumdmdlem  30780  cvrat4  37457  2reuimp  44607  sprsymrelfolem2  44945  reupr  44974