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Theorem imim3i 59
Description: Inference adding three nested antecedents. (Contributed by NM, 19-Dec-2006.)
Hypothesis
Ref Expression
imim3i.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
imim3i  |-  ( ( th  ->  ph )  -> 
( ( th  ->  ps )  ->  ( th  ->  ch ) ) )

Proof of Theorem imim3i
StepHypRef Expression
1 imim3i.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21imim2i 14 . 2  |-  ( ( th  ->  ph )  -> 
( th  ->  ( ps  ->  ch ) ) )
32a2d 26 1  |-  ( ( th  ->  ph )  -> 
( ( th  ->  ps )  ->  ( th  ->  ch ) ) )
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:  pm2.83  77  pm5.74  244  bi3antOLD  289  pm3.43i  456  ral2imi  2814  ceqsalt  3101  pm10.57  29791  ee33  31578  bj-bi3ant  32467  bj-ceqsalt0  32736  bj-ceqsalt1  32737
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