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Theorem sylanr2 397
Description: A syllogism inference. (Contributed by NM, 9-Apr-2005.)
Hypotheses
Ref Expression
sylanr2.1  |-  ( ph  ->  th )
sylanr2.2  |-  ( ( ps  /\  ( ch 
/\  th ) )  ->  ta )
Assertion
Ref Expression
sylanr2  |-  ( ( ps  /\  ( ch 
/\  ph ) )  ->  ta )

Proof of Theorem sylanr2
StepHypRef Expression
1 sylanr2.1 . . 3  |-  ( ph  ->  th )
21anim2i 334 . 2  |-  ( ( ch  /\  ph )  ->  ( ch  /\  th ) )
3 sylanr2.2 . 2  |-  ( ( ps  /\  ( ch 
/\  th ) )  ->  ta )
42, 3sylan2 280 1  |-  ( ( ps  /\  ( ch 
/\  ph ) )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem is referenced by:  adantrrl  470  adantrrr  471  1stconst  5873  2ndconst  5874  ltexprlemopl  6853  ltexprlemopu  6855  mulsub  7572  fzsubel  9154  expsubap  9621
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