Theorem 3exp1 1359

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 413	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 → 𝜏))
3	2	3exp 1125	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Syntax hints:   → wi 4   ∧ wa 396   ∧ w3a 1092

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 208  df-an 397  df-3an 1094

This theorem is referenced by:  3an1rs  1366  funelss  7989  ltmpi  10818  cshf1  14763  lcmfunsnlem  16601  mulgaddcom  19065  mulginvcom  19066  symgfvne  19347  voliunlem3  25537  3cyclfrgrrn  30374  numclwwlk1lem2foa  30442  frgrregord013  30483  strlem3a  32341  hstrlem3a  32349  chirredlem1  32479  nn0prpwlem  36550  matunitlindflem1  37983  zerdivemp1x  38314  athgt  39948  paddasslem14  40325  paddidm  40333  tendospcanN  41515  jm2.26  43447  relexpxpmin  44161  0ellimcdiv  46092  uhgrimisgrgric  48422  clnbgrgrimlem  48424