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  6315  omordi  8603  omwordri  8609  omass  8617  oewordri  8629  umgrclwwlkge2  30020  upgr4cycl4dv4e  30214  elspansn5  31603  atcvat3i  32425  mdsymlem5  32436  sumdmdlem  32447  cvrat4  39426  2reuimp  47065  sprsymrelfolem2  47418  reupr  47447  grtriprop  47846  isubgr3stgrlem6  47874