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Theorem eqtr2 2371
 Description: A transitive law for class equality. (Contributed by NM, 20-May-2005.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Assertion
Ref Expression
eqtr2 ((A = B A = C) → B = C)

Proof of Theorem eqtr2
StepHypRef Expression
1 eqcom 2355 . 2 (A = BB = A)
2 eqtr 2370 . 2 ((B = A A = C) → B = C)
31, 2sylanb 458 1 ((A = B A = C) → B = 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:  eqvinc  2966  dfxp2  5113  1stfo  5505  2ndfo  5506  swapf1o  5511  brtxp  5783  enprmaplem3  6078  peano4nc  6150  nchoicelem17  6305  fnfrec  6320
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