ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  eqtr2i Unicode version

Theorem eqtr2i 2199
Description: An equality transitivity inference. (Contributed by NM, 21-Feb-1995.)
Hypotheses
Ref Expression
eqtr2i.1  |-  A  =  B
eqtr2i.2  |-  B  =  C
Assertion
Ref Expression
eqtr2i  |-  C  =  A

Proof of Theorem eqtr2i
StepHypRef Expression
1 eqtr2i.1 . . 3  |-  A  =  B
2 eqtr2i.2 . . 3  |-  B  =  C
31, 2eqtri 2198 . 2  |-  A  =  C
43eqcomi 2181 1  |-  C  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1353
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-4 1510  ax-17 1526  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-cleq 2170
This theorem is referenced by:  3eqtrri  2203  3eqtr2ri  2205  symdif1  3400  dfif3  3547  dfsn2  3606  prprc1  3700  ruv  4549  xpindi  4762  xpindir  4763  dmcnvcnv  4851  rncnvcnv  4852  imainrect  5074  dfrn4  5089  fcoi1  5396  foimacnv  5479  fsnunfv  5717  dfoprab3  6191  fiintim  6927  sbthlemi8  6962  pitonnlem1  7843  ixi  8538  recexaplem2  8607  zeo  9356  num0h  9393  dec10p  9424  fseq1p1m1  10091  fsumrelem  11474  ef0lem  11663  ef01bndlem  11759  3lcm2e6woprm  12080  strsl0  12505  0g0  12749  tgioo  13939  tgqioo  13940  dveflem  14080  sincos4thpi  14154  coskpi  14162
  Copyright terms: Public domain W3C validator