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Theorem eel0001 36503
Description: An elimination deduction. (Contributed by Alan Sare, 17-Oct-2017.)
Hypotheses
Ref Expression
eel0001.1  |-  ph
eel0001.2  |-  ps
eel0001.3  |-  ch
eel0001.4  |-  ( th 
->  ta )
eel0001.5  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  ta )  ->  et )
Assertion
Ref Expression
eel0001  |-  ( th 
->  et )

Proof of Theorem eel0001
StepHypRef Expression
1 eel0001.3 . 2  |-  ch
2 eel0001.4 . 2  |-  ( th 
->  ta )
3 eel0001.1 . . 3  |-  ph
4 eel0001.2 . . 3  |-  ps
5 eel0001.5 . . . 4  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  ta )  ->  et )
65exp41 608 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ta  ->  et ) ) ) )
73, 4, 6mp2 9 . 2  |-  ( ch 
->  ( ta  ->  et ) )
81, 2, 7mpsyl 62 1  |-  ( th 
->  et )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367
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 369
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator