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  7982  ltmpi  10798  cshf1  14716  lcmfunsnlem  16552  mulgaddcom  18977  mulginvcom  18978  symgfvne  19260  voliunlem3  25451  3cyclfrgrrn  30230  numclwwlk1lem2foa  30298  frgrregord013  30339  strlem3a  32196  hstrlem3a  32204  chirredlem1  32334  nn0prpwlem  36306  matunitlindflem1  37606  zerdivemp1x  37937  athgt  39445  paddasslem14  39822  paddidm  39830  tendospcanN  41012  jm2.26  42985  relexpxpmin  43700  0ellimcdiv  45640  uhgrimisgrgric  47925  clnbgrgrimlem  47927