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

Theorem 3eqtrri 2062
 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 2057 . 2 A = 𝐶
4 3eqtri.3 . 2 𝐶 = 𝐷
53, 4eqtr2i 2058 1 𝐷 = A
 Colors of variables: wff set class Syntax hints:   = wceq 1242 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-cleq 2030 This theorem is referenced by:  dfdm2  4795  cofunex2g  5681  df1st2  5782  df2nd2  5783  enq0enq  6414  dfn2  7970
 Copyright terms: Public domain W3C validator