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Theorem sylanr1 401
Description: A syllogism inference. (Contributed by NM, 9-Apr-2005.)
Hypotheses
Ref Expression
sylanr1.1  |-  ( ph  ->  ch )
sylanr1.2  |-  ( ( ps  /\  ( ch 
/\  th ) )  ->  ta )
Assertion
Ref Expression
sylanr1  |-  ( ( ps  /\  ( ph  /\ 
th ) )  ->  ta )

Proof of Theorem sylanr1
StepHypRef Expression
1 sylanr1.1 . . 3  |-  ( ph  ->  ch )
21anim1i 338 . 2  |-  ( (
ph  /\  th )  ->  ( ch  /\  th ) )
3 sylanr1.2 . 2  |-  ( ( ps  /\  ( ch 
/\  th ) )  ->  ta )
42, 3sylan2 284 1  |-  ( ( ps  /\  ( ph  /\ 
th ) )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by:  adantrll  475  adantrlr  476  blsscls2  12651
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