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  6106  isinf  9214  isinfOLD  9215  infssuni  9304  fin1a2lem10  10369  elfz1b  13561  bernneq  14201  expnngt1  14213  swrdco  14810  dfgcd2  16523  lmodvsmmulgdi  20810  mamufacex  22290  gausslemma2dlem1a  27283  ssltun1  27727  ssltright  27790  expsgt0  28329  upgrewlkle2  29541  pthdivtx  29664  clwwlkinwwlk  29976  upgr3v3e3cycl  30116  upgr4cycl4dv4e  30121  numclwwlk2lem1lem  30278  frgrregord013  30331  ax6e2ndeqALT  44927  fmtnofac2  47574