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  8046  ltmpi  10918  cshf1  14828  lcmfunsnlem  16660  mulgaddcom  19081  mulginvcom  19082  symgfvne  19362  voliunlem3  25505  3cyclfrgrrn  30267  numclwwlk1lem2foa  30335  frgrregord013  30376  strlem3a  32233  hstrlem3a  32241  chirredlem1  32371  nn0prpwlem  36340  matunitlindflem1  37640  zerdivemp1x  37971  athgt  39475  paddasslem14  39852  paddidm  39860  tendospcanN  41042  jm2.26  43026  relexpxpmin  43741  0ellimcdiv  45678  uhgrimisgrgric  47944  clnbgrgrimlem  47946