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Theorem pm2.83 80
Description: Theorem *2.83 of [WhiteheadRussell] p. 108. Closed form of syld 45. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm2.83  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( ph  ->  ( ch 
->  th ) )  -> 
( ph  ->  ( ps 
->  th ) ) ) )

Proof of Theorem pm2.83
StepHypRef Expression
1 imim1 79 . 2  |-  ( ( ps  ->  ch )  ->  ( ( ch  ->  th )  ->  ( ps  ->  th ) ) )
21imim3i 61 1  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( ph  ->  ( ch 
->  th ) )  -> 
( ph  ->  ( ps 
->  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:  rexrsb  37990
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