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 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  1360  funelss  8072  ltmpi  10944  cshf1  14848  lcmfunsnlem  16678  mulgaddcom  19116  mulginvcom  19117  symgfvne  19398  voliunlem3  25587  3cyclfrgrrn  30305  numclwwlk1lem2foa  30373  frgrregord013  30414  strlem3a  32271  hstrlem3a  32279  chirredlem1  32409  nn0prpwlem  36323  matunitlindflem1  37623  zerdivemp1x  37954  athgt  39458  paddasslem14  39835  paddidm  39843  tendospcanN  41025  jm2.26  43014  relexpxpmin  43730  0ellimcdiv  45664  uhgrimisgrgric  47899  clnbgrgrimlem  47901