Theorem 3imp21 1114

Description: The importation inference 3imp 1111 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 1124 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 1113	1 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1087

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 1089

This theorem is referenced by:  3com12  1124  sotri3  6095  isinf  9177  infssuni  9258  fin1a2lem10  10331  elfz1b  13521  bernneq  14164  expnngt1  14176  swrdco  14772  dfgcd2  16485  lmodvsmmulgdi  20860  mamufacex  22352  gausslemma2dlem1a  27344  sltsun1  27796  sltsright  27869  expsgt0  28445  bdaypw2n0bnd  28472  upgrewlkle2  29692  pthdivtx  29812  clwwlkinwwlk  30127  upgr3v3e3cycl  30267  upgr4cycl4dv4e  30272  numclwwlk2lem1lem  30429  frgrregord013  30482  ax6e2ndeqALT  45286  fmtnofac2  47929