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  6085  isinf  9163  infssuni  9244  fin1a2lem10  10317  elfz1b  13507  bernneq  14150  expnngt1  14162  swrdco  14758  dfgcd2  16471  lmodvsmmulgdi  20846  mamufacex  22338  gausslemma2dlem1a  27330  ssltun1  27776  ssltright  27843  expsgt0  28395  upgrewlkle2  29629  pthdivtx  29749  clwwlkinwwlk  30064  upgr3v3e3cycl  30204  upgr4cycl4dv4e  30209  numclwwlk2lem1lem  30366  frgrregord013  30419  ax6e2ndeqALT  45113  fmtnofac2  47757