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  8026  ltmpi  10857  cshf1  14775  lcmfunsnlem  16611  mulgaddcom  19030  mulginvcom  19031  symgfvne  19311  voliunlem3  25453  3cyclfrgrrn  30215  numclwwlk1lem2foa  30283  frgrregord013  30324  strlem3a  32181  hstrlem3a  32189  chirredlem1  32319  nn0prpwlem  36310  matunitlindflem1  37610  zerdivemp1x  37941  athgt  39450  paddasslem14  39827  paddidm  39835  tendospcanN  41017  jm2.26  42991  relexpxpmin  43706  0ellimcdiv  45647  uhgrimisgrgric  47931  clnbgrgrimlem  47933