Theorem 3imp231 1113

Description: Importation inference. (Contributed by Alan Sare, 17-Oct-2017.)

Hypothesis

Ref	Expression
3imp.1	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

Assertion

Ref	Expression
3imp231	⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → 𝜃)

Proof of Theorem 3imp231

Step	Hyp	Ref	Expression
1		3imp.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2	1	com3l 89	. 2 ⊢ (𝜓 → (𝜒 → (𝜑 → 𝜃)))
3	2	3imp 1111	1 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → 𝜃)

Syntax hints:   → wi 4   ∧ 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:  3imp21  1114  sotri2  6094  oawordri  8487  undifixp  8884  sltstr  27795  sltsun2  27797  sltsleft  27868  expsne0  28444  eel12131  45068  odd2prm2  48078