MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  3imp31 Structured version   Visualization version   GIF version

Theorem 3imp31 1113
Description: The importation inference 3imp 1112 with commutation of the first and third conjuncts of the assertion relative to the hypothesis. (Contributed by Alan Sare, 11-Sep-2016.)
Hypothesis
Ref Expression
3imp.1 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
3imp31 ((𝜒𝜓𝜑) → 𝜃)

Proof of Theorem 3imp31
StepHypRef Expression
1 3imp.1 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
21com13 88 . 2 (𝜒 → (𝜓 → (𝜑𝜃)))
323imp 1112 1 ((𝜒𝜓𝜑) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1088
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 206  df-an 398  df-3an 1090
This theorem is referenced by:  3com13  1125  dvdsmodexp  16152  gsummatr01lem4  22030  elntg2  27983  pthdadjvtx  28727  umgr2cwwk2dif  29057  frgrwopreglem2  29306  relexpxpmin  42081  prproropf1olem4  45788  resum2sqorgt0  46885
  Copyright terms: Public domain W3C validator