Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  3imp231 Unicode version

Theorem 3imp231 28907
Description: Importation inference. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
3imp231.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
Assertion
Ref Expression
3imp231  |-  ( ( ps  /\  ch  /\  ph )  ->  th )

Proof of Theorem 3imp231
StepHypRef Expression
1 3imp231.1 . . . 4  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
21com12 27 . . 3  |-  ( ps 
->  ( ph  ->  ( ch  ->  th ) ) )
32com23 72 . 2  |-  ( ps 
->  ( ch  ->  ( ph  ->  th ) ) )
433imp 1145 1  |-  ( ( ps  /\  ch  /\  ph )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 934
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
  Copyright terms: Public domain W3C validator