Theorem 3imp31 1129

Description: The importation inference 3imp 1128 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 89	. 2 ⊢ (𝜒 → (𝜓 → (𝜑 → 𝜃)))
3	2	3imp 1128	1 ⊢ ((𝜒 ∧ 𝜓 ∧ 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:  3com13  1142  dvdsmodexp  16430  gsummatr01lem4  22973  elntg2  29563  pthdadjvtx  30313  umgr2cwwk2dif  30655  frgrwopreglem2  30914  relexpxpmin  44716  prproropf1olem4  48587  grimuhgr  48984  grlimgrtrilem2  49099  resum2sqorgt0  49820