Theorem imp41 424

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

Hypothesis

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

Assertion

Ref	Expression
imp41	⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)

Proof of Theorem imp41

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))
2	1	imp 405	. 2 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → (𝜃 → 𝜏)))
3	2	imp31 416	1 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)

Syntax hints:   → wi 4   ∧ wa 394

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 395

This theorem is referenced by:  3anassrs  1357  ad5ant125  1363  ad5ant2345  1367  peano5  7900  peano5OLD  7901  oelim  8555  lemul12a  12105  uzwo  12928  elfznelfzo  13773  injresinj  13789  swrdswrd  14691  2cshwcshw  14812  dvdsprmpweqle  16858  catidd  17663  grpinveu  18939  2ndcctbss  23403  rusgrnumwwlks  29857  erclwwlktr  29904  wwlksext2clwwlk  29939  erclwwlkntr  29953  grpoinveu  30401  spansncvi  31534  sumdmdii  32297  relowlpssretop  36971  matunitlindflem1  37217  unichnidl  37632  linepsubN  39352  pmapsub  39368  cdlemkid4  40534  hbtlem2  42687  2reu8i  46628  ply1mulgsumlem2  47638