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Theorem eqtr 2370
 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 2359 . 2 (A = B → (A = CB = C))
21biimpar 471 1 ((A = B B = C) → A = C)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   = wceq 1642 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346 This theorem is referenced by:  eqtr2  2371  eqtr3  2372  sylan9eq  2405  eqvinc  2966  uneqdifeq  3638  ider  5943  eqer  5961  ncaddccl  6144  ncdisjeq  6148  nchoicelem17  6305
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