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

Theorem 3eqtrri 2143
Description: An inference from three chained equalities. (Contributed by NM, 3-Aug-2006.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypotheses
Ref Expression
3eqtri.1  |-  A  =  B
3eqtri.2  |-  B  =  C
3eqtri.3  |-  C  =  D
Assertion
Ref Expression
3eqtrri  |-  D  =  A

Proof of Theorem 3eqtrri
StepHypRef Expression
1 3eqtri.1 . . 3  |-  A  =  B
2 3eqtri.2 . . 3  |-  B  =  C
31, 2eqtri 2138 . 2  |-  A  =  C
4 3eqtri.3 . 2  |-  C  =  D
53, 4eqtr2i 2139 1  |-  D  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1316
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-4 1472  ax-17 1491  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-cleq 2110
This theorem is referenced by:  resindm  4831  dfdm2  5043  cofunex2g  5978  df1st2  6084  df2nd2  6085  enq0enq  7207  dfn2  8958  9p1e10  9152  0.999...  11258  sincosq3sgn  12836  sincosq4sgn  12837
  Copyright terms: Public domain W3C validator