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Theorem eel0000 32813
Description: Elimination rule similar to mp4an 673, except with a left-nested conjunction unification theorem. (Contributed by Alan Sare, 17-Oct-2017.)
Hypotheses
Ref Expression
eel0000.1  |-  ph
eel0000.2  |-  ps
eel0000.3  |-  ch
eel0000.4  |-  th
eel0000.5  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  th )  ->  ta )
Assertion
Ref Expression
eel0000  |-  ta

Proof of Theorem eel0000
StepHypRef Expression
1 eel0000.3 . 2  |-  ch
2 eel0000.4 . 2  |-  th
3 eel0000.1 . . 3  |-  ph
4 eel0000.2 . . 3  |-  ps
5 eel0000.5 . . . 4  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  th )  ->  ta )
65exp41 610 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
73, 4, 6mp2 9 . 2  |-  ( ch 
->  ( th  ->  ta ) )
81, 2, 7mp2 9 1  |-  ta
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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