Theorem 3exp1 1351

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 1118	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  1358  funelss  8070  ltmpi  10941  cshf1  14844  lcmfunsnlem  16674  mulgaddcom  19128  mulginvcom  19129  symgfvne  19412  voliunlem3  25600  3cyclfrgrrn  30314  numclwwlk1lem2foa  30382  frgrregord013  30423  strlem3a  32280  hstrlem3a  32288  chirredlem1  32418  nn0prpwlem  36304  matunitlindflem1  37602  zerdivemp1x  37933  athgt  39438  paddasslem14  39815  paddidm  39823  tendospcanN  41005  jm2.26  42990  relexpxpmin  43706  0ellimcdiv  45604  uhgrimisgrgric  47836  clnbgrgrimlem  47838