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

Theorem eelTT 28883
Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eelTT.1  |-  (  T. 
->  ph )
eelTT.2  |-  (  T. 
->  ps )
eelTT.3  |-  ( (
ph  /\  ps )  ->  ch )
Assertion
Ref Expression
eelTT  |-  ch

Proof of Theorem eelTT
StepHypRef Expression
1 eelTT.2 . . 3  |-  (  T. 
->  ps )
2 truan 1340 . . . 4  |-  ( (  T.  /\  ps )  <->  ps )
3 eelTT.1 . . . . 5  |-  (  T. 
->  ph )
4 eelTT.3 . . . . 5  |-  ( (
ph  /\  ps )  ->  ch )
53, 4sylan 458 . . . 4  |-  ( (  T.  /\  ps )  ->  ch )
62, 5sylbir 205 . . 3  |-  ( ps 
->  ch )
71, 6syl 16 . 2  |-  (  T. 
->  ch )
87trud 1332 1  |-  ch
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359    T. wtru 1325
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 178  df-an 361  df-tru 1328
  Copyright terms: Public domain W3C validator