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Theorem tbsyl 24820
Description: The weak syllogism from Tarski-Bernays'. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
tbsyl.1  |-  ( ph  ->  ps )
tbsyl.2  |-  ( ps 
->  ch )
Assertion
Ref Expression
tbsyl  |-  ( ph  ->  ch )

Proof of Theorem tbsyl
StepHypRef Expression
1 tbsyl.2 . 2  |-  ( ps 
->  ch )
2 tbsyl.1 . . 3  |-  ( ph  ->  ps )
3 tb-ax1 24817 . . 3  |-  ( (
ph  ->  ps )  -> 
( ( ps  ->  ch )  ->  ( ph  ->  ch ) ) )
42, 3ax-mp 8 . 2  |-  ( ( ps  ->  ch )  ->  ( ph  ->  ch ) )
51, 4ax-mp 8 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  re1ax2lem  24821  re1ax2  24822
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
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