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Theorem imim2 55
Description: A closed form of syllogism (see syl 14). 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 19 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ps )
)
21imim2d 54 1  |-  ( (
ph  ->  ps )  -> 
( ( ch  ->  ph )  ->  ( ch  ->  ps ) ) )
Colors of variables: wff set 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:  syldd  67  pm3.34  341  const  820  spimth  1696  spsbim  1797  bj-stim  12788  elabgft1  12819  bj-rspgt  12827  bj-findis  13011
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