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  6076  isinf  9149  infssuni  9230  fin1a2lem10  10300  elfz1b  13493  bernneq  14136  expnngt1  14148  swrdco  14744  dfgcd2  16457  lmodvsmmulgdi  20830  mamufacex  22311  gausslemma2dlem1a  27303  ssltun1  27749  ssltright  27816  expsgt0  28360  upgrewlkle2  29585  pthdivtx  29705  clwwlkinwwlk  30020  upgr3v3e3cycl  30160  upgr4cycl4dv4e  30165  numclwwlk2lem1lem  30322  frgrregord013  30375  ax6e2ndeqALT  44971  fmtnofac2  47608