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  7989  ltmpi  10813  cshf1  14731  lcmfunsnlem  16566  mulgaddcom  19026  mulginvcom  19027  symgfvne  19308  voliunlem3  25507  3cyclfrgrrn  30310  numclwwlk1lem2foa  30378  frgrregord013  30419  strlem3a  32276  hstrlem3a  32284  chirredlem1  32414  nn0prpwlem  36465  matunitlindflem1  37756  zerdivemp1x  38087  athgt  39655  paddasslem14  40032  paddidm  40040  tendospcanN  41222  jm2.26  43186  relexpxpmin  43900  0ellimcdiv  45835  uhgrimisgrgric  48119  clnbgrgrimlem  48121