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Theorem imim2 51
Description: A closed form of syllogism (see syl 17). Theorem *2.05 of [WhiteheadRussell] p. 100. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 6-Sep-2012.)
Assertion
Ref Expression
imim2  |-  ( (
ph  ->  ps )  -> 
( ( ch  ->  ph )  ->  ( ch  ->  ps ) ) )

Proof of Theorem imim2
StepHypRef Expression
1 id 21 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ps )
)
21imim2d 50 1  |-  ( (
ph  ->  ps )  -> 
( ( ch  ->  ph )  ->  ( ch  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6
This theorem is referenced by:  syldd  63  pm3.34  572  19.41rgVD  27691
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-mp 10
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