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Theorem 3eqtr4ri 2171
Description: An inference from three chained equalities. (Contributed by NM, 2-Sep-1995.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypotheses
Ref Expression
3eqtr4i.1  |-  A  =  B
3eqtr4i.2  |-  C  =  A
3eqtr4i.3  |-  D  =  B
Assertion
Ref Expression
3eqtr4ri  |-  D  =  C

Proof of Theorem 3eqtr4ri
StepHypRef Expression
1 3eqtr4i.3 . . 3  |-  D  =  B
2 3eqtr4i.1 . . 3  |-  A  =  B
31, 2eqtr4i 2163 . 2  |-  D  =  A
4 3eqtr4i.2 . 2  |-  C  =  A
53, 4eqtr4i 2163 1  |-  D  =  C
Colors of variables: wff set class
Syntax hints:    = wceq 1331
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 1423  ax-gen 1425  ax-4 1487  ax-17 1506  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-cleq 2132
This theorem is referenced by:  cbvreucsf  3064  dfif6  3476  qdass  3620  tpidm12  3622  unipr  3750  dfdm4  4731  dmun  4746  resres  4831  inres  4836  resdifcom  4837  resiun1  4838  imainrect  4984  coundi  5040  coundir  5041  funopg  5157  offres  6033  mpomptsx  6095  cnvoprab  6131  snec  6490  halfpm6th  8947  numsucc  9228  decbin2  9329  fsumadd  11182  fsum2d  11211  znnen  11918
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