Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  eelT00 Unicode version

Theorem eelT00 28480
Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eelT00.1  |-  (  T. 
->  ph )
eelT00.2  |-  ps
eelT00.3  |-  ch
eelT00.4  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Assertion
Ref Expression
eelT00  |-  th

Proof of Theorem eelT00
StepHypRef Expression
1 eelT00.3 . 2  |-  ch
2 eelT00.2 . . 3  |-  ps
3 3anass 938 . . . . 5  |-  ( (  T.  /\  ps  /\  ch )  <->  (  T.  /\  ( ps  /\  ch )
) )
4 trcrm 24951 . . . . 5  |-  ( (  T.  /\  ( ps 
/\  ch ) )  <->  ( ps  /\ 
ch ) )
53, 4bitri 240 . . . 4  |-  ( (  T.  /\  ps  /\  ch )  <->  ( ps  /\  ch ) )
6 eelT00.1 . . . . 5  |-  (  T. 
->  ph )
7 eelT00.4 . . . . 5  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
86, 7syl3an1 1215 . . . 4  |-  ( (  T.  /\  ps  /\  ch )  ->  th )
95, 8sylbir 204 . . 3  |-  ( ( ps  /\  ch )  ->  th )
102, 9mpan 651 . 2  |-  ( ch 
->  th )
111, 10ax-mp 8 1  |-  th
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934    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-3an 936  df-tru 1310
  Copyright terms: Public domain W3C validator