Theorem 3imp31 1124

Description: The importation inference 3imp 1123 with commutation of the first and third conjuncts of the assertion relative to the hypothesis. (Contributed by Alan Sare, 11-Sep-2016.)

Hypothesis

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

Assertion

Ref	Expression
3imp31	⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) → 𝜃)

Proof of Theorem 3imp31

Step	Hyp	Ref	Expression
1		3imp.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2	1	com13 88	. 2 ⊢ (𝜒 → (𝜓 → (𝜑 → 𝜃)))
3	2	3imp 1123	1 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1098

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 209  df-an 400  df-3an 1100

This theorem is referenced by:  3com13  1137  dvdsmodexp  16294  gsummatr01lem4  22718  elntg2  29186  pthdadjvtx  29928  umgr2cwwk2dif  30266  frgrwopreglem2  30515  relexpxpmin  44293  prproropf1olem4  48112  grimuhgr  48509  grlimgrtrilem2  48624  resum2sqorgt0  49331