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  19012  mulginvcom  19013  symgfvne  19295  voliunlem3  25486  3cyclfrgrrn  30265  numclwwlk1lem2foa  30333  frgrregord013  30374  strlem3a  32231  hstrlem3a  32239  chirredlem1  32369  nn0prpwlem  36303  matunitlindflem1  37603  zerdivemp1x  37934  athgt  39443  paddasslem14  39820  paddidm  39828  tendospcanN  41010  jm2.26  42984  relexpxpmin  43699  0ellimcdiv  45640  uhgrimisgrgric  47924  clnbgrgrimlem  47926