Theorem 3exp1 1354

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 1120	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1087

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 1089

This theorem is referenced by:  3an1rs  1361  funelss  8001  ltmpi  10827  cshf1  14745  lcmfunsnlem  16580  mulgaddcom  19040  mulginvcom  19041  symgfvne  19322  voliunlem3  25521  3cyclfrgrrn  30373  numclwwlk1lem2foa  30441  frgrregord013  30482  strlem3a  32340  hstrlem3a  32348  chirredlem1  32478  nn0prpwlem  36538  matunitlindflem1  37867  zerdivemp1x  38198  athgt  39832  paddasslem14  40209  paddidm  40217  tendospcanN  41399  jm2.26  43359  relexpxpmin  44073  0ellimcdiv  46007  uhgrimisgrgric  48291  clnbgrgrimlem  48293