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Theorem imim12 100
Description: Closed form of imim12i 59 and of 3syl 18. (Contributed by BJ, 16-Jul-2019.)
Assertion
Ref Expression
imim12  |-  ( (
ph  ->  ps )  -> 
( ( ch  ->  th )  ->  ( ( ps  ->  ch )  -> 
( ph  ->  th )
) ) )

Proof of Theorem imim12
StepHypRef Expression
1 imim2 55 . . . 4  |-  ( ( ch  ->  th )  ->  ( ( ps  ->  ch )  ->  ( ps  ->  th ) ) )
21com13 83 . . 3  |-  ( ps 
->  ( ( ps  ->  ch )  ->  ( ( ch  ->  th )  ->  th )
) )
32imim2i 16 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ( ps  ->  ch )  ->  ( ( ch  ->  th )  ->  th )
) ) )
43com24 90 1  |-  ( (
ph  ->  ps )  -> 
( ( ch  ->  th )  ->  ( ( ps  ->  ch )  -> 
( ph  ->  th )
) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by: (None)
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