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Theorem eel0TT 28479
Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eel0TT.1  |-  ph
eel0TT.2  |-  (  T. 
->  ps )
eel0TT.3  |-  (  T. 
->  ch )
eel0TT.4  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Assertion
Ref Expression
eel0TT  |-  th

Proof of Theorem eel0TT
StepHypRef Expression
1 eel0TT.3 . . 3  |-  (  T. 
->  ch )
2 trcrm 24951 . . . 4  |-  ( (  T.  /\  ch )  <->  ch )
3 eel0TT.2 . . . . 5  |-  (  T. 
->  ps )
4 eel0TT.1 . . . . . 6  |-  ph
5 eel0TT.4 . . . . . 6  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
64, 5mp3an1 1264 . . . . 5  |-  ( ( ps  /\  ch )  ->  th )
73, 6sylan 457 . . . 4  |-  ( (  T.  /\  ch )  ->  th )
82, 7sylbir 204 . . 3  |-  ( ch 
->  th )
91, 8syl 15 . 2  |-  (  T. 
->  th )
109trud 1314 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
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