Users' Mathboxes Mathbox for Jeff Madsen < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  syldanl Unicode version

Theorem syldanl 26334
Description: A syllogism deduction with conjoined antecedents. (Contributed by Jeff Madsen, 20-Jun-2011.)
Hypotheses
Ref Expression
syldanl.1  |-  ( (
ph  /\  ps )  ->  ch )
syldanl.2  |-  ( ( ( ph  /\  ch )  /\  th )  ->  ta )
Assertion
Ref Expression
syldanl  |-  ( ( ( ph  /\  ps )  /\  th )  ->  ta )

Proof of Theorem syldanl
StepHypRef Expression
1 syldanl.1 . . . 4  |-  ( (
ph  /\  ps )  ->  ch )
21ex 423 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
32imdistani 671 . 2  |-  ( (
ph  /\  ps )  ->  ( ph  /\  ch ) )
4 syldanl.2 . 2  |-  ( ( ( ph  /\  ch )  /\  th )  ->  ta )
53, 4sylan 457 1  |-  ( ( ( ph  /\  ps )  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  heibor1lem  26533  idlnegcl  26647  igenmin  26689
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
  Copyright terms: Public domain W3C validator