Theorem 3imp21 1105

Description: The importation inference 3imp 1101 with commutation of the first and second conjuncts of the assertion relative to the hypothesis. (Contributed by Alan Sare, 11-Sep-2016.) (Revised to shorten 3com12 1117 by Wolf Lammen, 23-Jun-2022.)

Hypothesis

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

Assertion

Ref	Expression
3imp21	⊢ ((𝜓 ∧ 𝜑 ∧ 𝜒) → 𝜃)

Proof of Theorem 3imp21

Step	Hyp	Ref	Expression
1		3imp.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2	1	com13 88	. 2 ⊢ (𝜒 → (𝜓 → (𝜑 → 𝜃)))
3	2	3imp231 1104	1 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1072

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 197  df-an 385  df-3an 1074

This theorem is referenced by:  3com12  1117  sotri3  5676  elfz1b  12594  gausslemma2dlem1a  25281  upgrewlkle2  26704  pthdivtx  26827  clwwlkinwwlk  27161  clwlksfclwwlkOLD  27208  upgr3v3e3cycl  27324  upgr4cycl4dv4e  27329  numclwwlk2lem1lem  27490  frgrregord013  27555  ax6e2ndeqALT  39658  fmtnofac2  41983