MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  3imp231 Structured version   Visualization version   GIF version

Theorem 3imp231 1104
Description: Importation inference. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
3imp.1 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
3imp231 ((𝜓𝜒𝜑) → 𝜃)

Proof of Theorem 3imp231
StepHypRef Expression
1 3imp.1 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
21com3l 89 . 2 (𝜓 → (𝜒 → (𝜑𝜃)))
323imp 1101 1 ((𝜓𝜒𝜑) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1071
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 197  df-an 383  df-3an 1073
This theorem is referenced by:  3imp21  1105  3imp3i2anOLD  1437  sotri2  5666  oawordri  7784  undifixp  8098  eel12131  39463  odd2prm2  42155
  Copyright terms: Public domain W3C validator