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Theorem eel0121 37062
Description: An elimination deduction. (Contributed by Alan Sare, 17-Oct-2017.)
Hypotheses
Ref Expression
eel0121.1  |-  ph
eel0121.2  |-  ( ps 
->  ch )
eel0121.3  |-  ( ( ps  /\  th )  ->  ta )
eel0121.4  |-  ( (
ph  /\  ch  /\  ta )  ->  et )
Assertion
Ref Expression
eel0121  |-  ( ( ps  /\  th )  ->  et )

Proof of Theorem eel0121
StepHypRef Expression
1 eel0121.1 . . 3  |-  ph
2 eel0121.2 . . 3  |-  ( ps 
->  ch )
3 eel0121.3 . . 3  |-  ( ( ps  /\  th )  ->  ta )
4 eel0121.4 . . 3  |-  ( (
ph  /\  ch  /\  ta )  ->  et )
51, 2, 3, 4eel012 37061 . 2  |-  ( ( ps  /\  ( ps 
/\  th ) )  ->  et )
65anabss5 823 1  |-  ( ( ps  /\  th )  ->  et )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 370    /\ w3a 982
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 188  df-an 372  df-3an 984
This theorem is referenced by:  isosctrlem1ALT  37304
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