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  6124  isinf  9273  isinfOLD  9274  infssuni  9363  fin1a2lem10  10428  elfz1b  13615  bernneq  14252  expnngt1  14264  swrdco  14861  dfgcd2  16570  lmodvsmmulgdi  20859  mamufacex  22339  gausslemma2dlem1a  27333  ssltun1  27777  ssltright  27840  expsgt0  28379  upgrewlkle2  29591  pthdivtx  29714  clwwlkinwwlk  30026  upgr3v3e3cycl  30166  upgr4cycl4dv4e  30171  numclwwlk2lem1lem  30328  frgrregord013  30381  ax6e2ndeqALT  44922  fmtnofac2  47550