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Theorem eqtr 2105
Description: Transitive law for class equality. Proposition 4.7(3) of [TakeutiZaring] p. 13. (Contributed by NM, 25-Jan-2004.)
Assertion
Ref Expression
eqtr  |-  ( ( A  =  B  /\  B  =  C )  ->  A  =  C )

Proof of Theorem eqtr
StepHypRef Expression
1 eqeq1 2094 . 2  |-  ( A  =  B  ->  ( A  =  C  <->  B  =  C ) )
21biimpar 291 1  |-  ( ( A  =  B  /\  B  =  C )  ->  A  =  C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    = wceq 1289
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-4 1445  ax-17 1464  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-cleq 2081
This theorem is referenced by:  eqtr2  2106  eqtr3  2107  sylan9eq  2140  eqvinc  2738  eqvincg  2739  uneqdifeqim  3364  preqsn  3614  dtruex  4365  relresfld  4947  relcoi1  4949  eqer  6304  xpiderm  6343  addlsub  7827  bj-findis  11531
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