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  6245  omordi  8487  omwordri  8493  omass  8501  oewordri  8513  umgrclwwlkge2  29973  upgr4cycl4dv4e  30167  elspansn5  31556  atcvat3i  32378  mdsymlem5  32389  sumdmdlem  32400  cvrat4  39563  2reuimp  47240  sprsymrelfolem2  47618  reupr  47647  grtriprop  48066  isubgr3stgrlem6  48096