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Theorem eel11111 31461
Description: 5 hypothesis elimination deduction for an assertion with a singleton virtual hypothesis collection. Similar to syl113anc 1230 except the unification theorem uses left-nested conjunction. (Contributed by Alan Sare, 17-Oct-2017.)
Hypotheses
Ref Expression
eel11111.1  |-  ( ph  ->  ps )
eel11111.2  |-  ( ph  ->  ch )
eel11111.3  |-  ( ph  ->  th )
eel11111.4  |-  ( ph  ->  ta )
eel11111.5  |-  ( ph  ->  et )
eel11111.6  |-  ( ( ( ( ( ps 
/\  ch )  /\  th )  /\  ta )  /\  et )  ->  ze )
Assertion
Ref Expression
eel11111  |-  ( ph  ->  ze )

Proof of Theorem eel11111
StepHypRef Expression
1 eel11111.4 . 2  |-  ( ph  ->  ta )
2 eel11111.5 . 2  |-  ( ph  ->  et )
3 eel11111.1 . . 3  |-  ( ph  ->  ps )
4 eel11111.2 . . 3  |-  ( ph  ->  ch )
5 eel11111.3 . . 3  |-  ( ph  ->  th )
6 eel11111.6 . . . . 5  |-  ( ( ( ( ( ps 
/\  ch )  /\  th )  /\  ta )  /\  et )  ->  ze )
76exp41 610 . . . 4  |-  ( ( ps  /\  ch )  ->  ( th  ->  ( ta  ->  ( et  ->  ze ) ) ) )
87ex 434 . . 3  |-  ( ps 
->  ( ch  ->  ( th  ->  ( ta  ->  ( et  ->  ze )
) ) ) )
93, 4, 5, 8syl3c 61 . 2  |-  ( ph  ->  ( ta  ->  ( et  ->  ze ) ) )
101, 2, 9mp2d 45 1  |-  ( ph  ->  ze )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
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
This theorem is referenced by: (None)
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