Theorem 3imp21 1113

Description: The importation inference 3imp 1110 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 1123 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 1112	1 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1086

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 1088

This theorem is referenced by:  3com12  1123  sotri3  6103  isinf  9207  isinfOLD  9208  infssuni  9297  fin1a2lem10  10362  elfz1b  13554  bernneq  14194  expnngt1  14206  swrdco  14803  dfgcd2  16516  lmodvsmmulgdi  20803  mamufacex  22283  gausslemma2dlem1a  27276  ssltun1  27720  ssltright  27783  expsgt0  28322  upgrewlkle2  29534  pthdivtx  29657  clwwlkinwwlk  29969  upgr3v3e3cycl  30109  upgr4cycl4dv4e  30114  numclwwlk2lem1lem  30271  frgrregord013  30324  ax6e2ndeqALT  44920  fmtnofac2  47570