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Theorem eqtr 2054
 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 2043 . 2 (A = B → (A = 𝐶B = 𝐶))
21biimpar 281 1 ((A = B B = 𝐶) → A = 𝐶)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   = 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:  eqtr2  2055  eqtr3  2056  sylan9eq  2089  eqvinc  2661  eqvincg  2662  uneqdifeqim  3302  preqsn  3537  dtruex  4237  relresfld  4790  relcoi1  4792  eqer  6074  xpiderm  6113  bj-findis  9439
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