Theorem imp4c 423

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 410	. 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜃 → 𝜏)))
3	2	impd 410	1 ⊢ (𝜑 → (((𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜏))

Syntax hints:   → wi 4   ∧ wa 395

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 207  df-an 396

This theorem is referenced by:  imp44  428  reuop  6324  omordi  8622  omwordri  8628  omass  8636  oewordri  8648  umgrclwwlkge2  30023  upgr4cycl4dv4e  30217  elspansn5  31606  atcvat3i  32428  mdsymlem5  32439  sumdmdlem  32450  cvrat4  39400  2reuimp  47030  sprsymrelfolem2  47367  reupr  47396  grtriprop  47792