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Theorem pm2.86i 92
Description: Inference based on pm2.86 94. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 3-Apr-2013.)
Hypothesis
Ref Expression
pm2.86i.1  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ch )
)
Assertion
Ref Expression
pm2.86i  |-  ( ph  ->  ( ps  ->  ch ) )

Proof of Theorem pm2.86i
StepHypRef Expression
1 ax-1 5 . . 3  |-  ( ps 
->  ( ph  ->  ps ) )
2 pm2.86i.1 . . 3  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ch )
)
31, 2syl 15 . 2  |-  ( ps 
->  ( ph  ->  ch ) )
43com12 27 1  |-  ( ph  ->  ( ps  ->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  stoweidlem17  27766
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
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