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Theorem sylanl2 395
Description: A syllogism inference. (Contributed by NM, 1-Jan-2005.)
Hypotheses
Ref Expression
sylanl2.1  |-  ( ph  ->  ch )
sylanl2.2  |-  ( ( ( ps  /\  ch )  /\  th )  ->  ta )
Assertion
Ref Expression
sylanl2  |-  ( ( ( ps  /\  ph )  /\  th )  ->  ta )

Proof of Theorem sylanl2
StepHypRef Expression
1 sylanl2.1 . . 3  |-  ( ph  ->  ch )
21anim2i 334 . 2  |-  ( ( ps  /\  ph )  ->  ( ps  /\  ch ) )
3 sylanl2.2 . 2  |-  ( ( ( ps  /\  ch )  /\  th )  ->  ta )
42, 3sylan 277 1  |-  ( ( ( ps  /\  ph )  /\  th )  ->  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:  mpanlr1  431  adantlrl  466  adantlrr  467  cnegexlem3  7596  mulsub  7816  divsubdivap  8127  modqcyc2  9688  lcmneg  10923
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