ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3ancoma Unicode version

Theorem 3ancoma 952
Description: Commutation law for triple conjunction. (Contributed by NM, 21-Apr-1994.)
Assertion
Ref Expression
3ancoma  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ph  /\ 
ch ) )

Proof of Theorem 3ancoma
StepHypRef Expression
1 ancom 264 . . 3  |-  ( (
ph  /\  ps )  <->  ( ps  /\  ph )
)
21anbi1i 451 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  <->  ( ( ps  /\  ph )  /\  ch ) )
3 df-3an 947 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ch )
)
4 df-3an 947 . 2  |-  ( ( ps  /\  ph  /\  ch )  <->  ( ( ps 
/\  ph )  /\  ch ) )
52, 3, 43bitr4i 211 1  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ph  /\ 
ch ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104    /\ w3a 945
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 depends on definitions:  df-bi 116  df-3an 947
This theorem is referenced by:  3ancomb  953  3anrev  955  3anan12  957  3com12  1168  elfzmlbp  9849  elfzo2  9867
  Copyright terms: Public domain W3C validator