Theorem 3imp231 1130

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 90	. 2 ⊢ (𝜓 → (𝜒 → (𝜑 → 𝜃)))
3	2	3imp 1128	1 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → 𝜃)

This proof depends on syntax axioms:   → wi 4   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  3imp21  1131  sotri2  6123  oawordri  8558  undifixp  8962  sltstr  28173  sltsun2  28175  sltsleft  28246  expsne0  28822  eel12131  45694  odd2prm2  48815