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  6091  isinf  9183  isinfOLD  9184  infssuni  9273  fin1a2lem10  10338  elfz1b  13530  bernneq  14170  expnngt1  14182  swrdco  14779  dfgcd2  16492  lmodvsmmulgdi  20835  mamufacex  22316  gausslemma2dlem1a  27309  ssltun1  27754  ssltright  27820  expsgt0  28364  upgrewlkle2  29587  pthdivtx  29707  clwwlkinwwlk  30019  upgr3v3e3cycl  30159  upgr4cycl4dv4e  30164  numclwwlk2lem1lem  30321  frgrregord013  30374  ax6e2ndeqALT  44913  fmtnofac2  47563