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  7979  ltmpi  10795  cshf1  14717  lcmfunsnlem  16552  mulgaddcom  19011  mulginvcom  19012  symgfvne  19293  voliunlem3  25480  3cyclfrgrrn  30266  numclwwlk1lem2foa  30334  frgrregord013  30375  strlem3a  32232  hstrlem3a  32240  chirredlem1  32370  nn0prpwlem  36366  matunitlindflem1  37666  zerdivemp1x  37997  athgt  39565  paddasslem14  39942  paddidm  39950  tendospcanN  41132  jm2.26  43105  relexpxpmin  43820  0ellimcdiv  45757  uhgrimisgrgric  48041  clnbgrgrimlem  48043