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Theorem eel00001 36522
Description: An elimination deduction. (Contributed by Alan Sare, 17-Oct-2017.)
Hypotheses
Ref Expression
eel00001.1  |-  ph
eel00001.2  |-  ps
eel00001.3  |-  ch
eel00001.4  |-  th
eel00001.5  |-  ( ta 
->  et )
eel00001.6  |-  ( ( ( ( ( ph  /\ 
ps )  /\  ch )  /\  th )  /\  et )  ->  ze )
Assertion
Ref Expression
eel00001  |-  ( ta 
->  ze )

Proof of Theorem eel00001
StepHypRef Expression
1 eel00001.5 . 2  |-  ( ta 
->  et )
2 eel00001.3 . . 3  |-  ch
3 eel00001.4 . . 3  |-  th
4 eel00001.1 . . . 4  |-  ph
5 eel00001.2 . . . 4  |-  ps
6 eel00001.6 . . . . 5  |-  ( ( ( ( ( ph  /\ 
ps )  /\  ch )  /\  th )  /\  et )  ->  ze )
76exp41 608 . . . 4  |-  ( (
ph  /\  ps )  ->  ( ch  ->  ( th  ->  ( et  ->  ze ) ) ) )
84, 5, 7mp2an 670 . . 3  |-  ( ch 
->  ( th  ->  ( et  ->  ze ) ) )
92, 3, 8mp2 9 . 2  |-  ( et 
->  ze )
101, 9syl 17 1  |-  ( ta 
->  ze )
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)
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