Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  eelT1 Unicode version

Theorem eelT1 28485
Description: Syllogism inference combined with modus ponens. (Contributed by Jeff Madsen, 2-Sep-2009.) (Revised by Alan Sare, 23-Dec-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eelT1.1  |-  (  T. 
->  ph )
eelT1.2  |-  ( ps 
->  ch )
eelT1.3  |-  ( (
ph  /\  ch )  ->  th )
Assertion
Ref Expression
eelT1  |-  ( ps 
->  th )

Proof of Theorem eelT1
StepHypRef Expression
1 eelT1.1 . . 3  |-  (  T. 
->  ph )
21trud 1314 . 2  |-  ph
3 eelT1.2 . 2  |-  ( ps 
->  ch )
4 eelT1.3 . 2  |-  ( (
ph  /\  ch )  ->  th )
52, 3, 4sylancr 644 1  |-  ( ps 
->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    T. wtru 1307
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-tru 1310
  Copyright terms: Public domain W3C validator