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  7994  ltmpi  10821  cshf1  14766  lcmfunsnlem  16604  mulgaddcom  19068  mulginvcom  19069  symgfvne  19350  voliunlem3  25532  3cyclfrgrrn  30374  numclwwlk1lem2foa  30442  frgrregord013  30483  strlem3a  32341  hstrlem3a  32349  chirredlem1  32479  nn0prpwlem  36523  matunitlindflem1  37954  zerdivemp1x  38285  athgt  39919  paddasslem14  40296  paddidm  40304  tendospcanN  41486  jm2.26  43451  relexpxpmin  44165  0ellimcdiv  46098  uhgrimisgrgric  48422  clnbgrgrimlem  48424