Theorem imp42 426

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

Hypothesis

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

Assertion

Ref	Expression
imp42	⊢ (((𝜑 ∧ (𝜓 ∧ 𝜒)) ∧ 𝜃) → 𝜏)

Proof of Theorem imp42

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))
2	1	imp32 418	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → (𝜃 → 𝜏))
3	2	imp 406	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 206  df-an 396

This theorem is referenced by:  imp55  442  ltexprlem7  10782  iscatd  17363  isposd  18022  pospropd  18026  mulgghm2  20679  ordtbaslem  22320  txbas  22699  frgrncvvdeqlem8  28649  grporcan  28859  chirredlem1  30731  cvxpconn  33183  cvxsconn  33184  nocvxminlem  33951  rngonegmn1l  36078  prnc  36204  reuopreuprim  44930