ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  syl32anc Unicode version

Theorem syl32anc 1143
Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
Hypotheses
Ref Expression
sylXanc.1  |-  ( ph  ->  ps )
sylXanc.2  |-  ( ph  ->  ch )
sylXanc.3  |-  ( ph  ->  th )
sylXanc.4  |-  ( ph  ->  ta )
sylXanc.5  |-  ( ph  ->  et )
syl32anc.6  |-  ( ( ( ps  /\  ch  /\ 
th )  /\  ( ta  /\  et ) )  ->  ze )
Assertion
Ref Expression
syl32anc  |-  ( ph  ->  ze )

Proof of Theorem syl32anc
StepHypRef Expression
1 sylXanc.1 . 2  |-  ( ph  ->  ps )
2 sylXanc.2 . 2  |-  ( ph  ->  ch )
3 sylXanc.3 . 2  |-  ( ph  ->  th )
4 sylXanc.4 . . 3  |-  ( ph  ->  ta )
5 sylXanc.5 . . 3  |-  ( ph  ->  et )
64, 5jca 290 . 2  |-  ( ph  ->  ( ta  /\  et ) )
7 syl32anc.6 . 2  |-  ( ( ( ps  /\  ch  /\ 
th )  /\  ( ta  /\  et ) )  ->  ze )
81, 2, 3, 6, 7syl31anc 1138 1  |-  ( ph  ->  ze )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 97    /\ w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 887
This theorem is referenced by:  exple1  9310  leexp2rd  9410
  Copyright terms: Public domain W3C validator