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Theorem eel0TT 31783
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 truan 1387 . . . 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 1302 . . . . 5  |-  ( ( ps  /\  ch )  ->  th )
73, 6sylan 471 . . . 4  |-  ( ( T.  /\  ch )  ->  th )
82, 7sylbir 213 . . 3  |-  ( ch 
->  th )
91, 8syl 16 . 2  |-  ( T. 
->  th )
109trud 1379 1  |-  th
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 965   T. wtru 1371
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 967  df-tru 1373
This theorem is referenced by: (None)
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