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  8005  ltmpi  10833  cshf1  14751  lcmfunsnlem  16587  mulgaddcom  19006  mulginvcom  19007  symgfvne  19287  voliunlem3  25429  3cyclfrgrrn  30188  numclwwlk1lem2foa  30256  frgrregord013  30297  strlem3a  32154  hstrlem3a  32162  chirredlem1  32292  nn0prpwlem  36283  matunitlindflem1  37583  zerdivemp1x  37914  athgt  39423  paddasslem14  39800  paddidm  39808  tendospcanN  40990  jm2.26  42964  relexpxpmin  43679  0ellimcdiv  45620  uhgrimisgrgric  47904  clnbgrgrimlem  47906