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  6079  isinf  9154  infssuni  9236  fin1a2lem10  10303  elfz1b  13496  bernneq  14136  expnngt1  14148  swrdco  14744  dfgcd2  16457  lmodvsmmulgdi  20800  mamufacex  22281  gausslemma2dlem1a  27274  ssltun1  27719  ssltright  27785  expsgt0  28329  upgrewlkle2  29552  pthdivtx  29672  clwwlkinwwlk  29984  upgr3v3e3cycl  30124  upgr4cycl4dv4e  30129  numclwwlk2lem1lem  30286  frgrregord013  30339  ax6e2ndeqALT  44904  fmtnofac2  47553