Theorem 3exp1 1353

Description: Exportation from left triple conjunction. (Contributed by NM, 24-Feb-2005.)

Hypothesis

Ref	Expression
3exp1.1	⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜏)

Assertion

Ref	Expression
3exp1	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Proof of Theorem 3exp1

Step	Hyp	Ref	Expression
1		3exp1.1	. . 3 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜏)
2	1	ex 412	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 → 𝜏))
3	2	3exp 1119	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1086

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  df-3an 1088

This theorem is referenced by:  3an1rs  1360  funelss  8029  ltmpi  10864  cshf1  14782  lcmfunsnlem  16618  mulgaddcom  19037  mulginvcom  19038  symgfvne  19318  voliunlem3  25460  3cyclfrgrrn  30222  numclwwlk1lem2foa  30290  frgrregord013  30331  strlem3a  32188  hstrlem3a  32196  chirredlem1  32326  nn0prpwlem  36317  matunitlindflem1  37617  zerdivemp1x  37948  athgt  39457  paddasslem14  39834  paddidm  39842  tendospcanN  41024  jm2.26  42998  relexpxpmin  43713  0ellimcdiv  45654  uhgrimisgrgric  47935  clnbgrgrimlem  47937