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Theorem eqtr3 2372
 Description: A transitive law for class equality. (Contributed by NM, 20-May-2005.)
Assertion
Ref Expression
eqtr3 ((A = C B = C) → A = B)

Proof of Theorem eqtr3
StepHypRef Expression
1 eqcom 2355 . 2 (B = CC = B)
2 eqtr 2370 . 2 ((A = C C = B) → A = B)
31, 2sylan2b 461 1 ((A = C B = C) → A = B)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   = wceq 1642 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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:  eueq  3008  euind  3023  reuind  3039  phialllem1  4616  xpcan  5057  xpcan2  5058  foco  5279  xpassen  6057  enmap2lem4  6066  enmap1lem4  6072  ncspw1eu  6159
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