MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  imim3i Unicode version

Theorem imim3i 55
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 13 . 2  |-  ( ( th  ->  ph )  -> 
( th  ->  ( ps  ->  ch ) ) )
32a2d 23 1  |-  ( ( th  ->  ph )  -> 
( ( th  ->  ps )  ->  ( th  ->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  pm2.83  71  pm5.74  235  bi3ant  280  pm3.43i  442  ax12olem3  1882  ceqsalt  2823  pm10.57  27669  ee33  28583  ax12olem3aAUX7  29434
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
  Copyright terms: Public domain W3C validator