Theorem eqtr3 2225

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

Step	Hyp	Ref	Expression
1		eqcom 2207	. 2 |- ( B = C <-> C = B )
2		eqtr 2223	. 2 |- ( ( A = C /\ C = B ) -> A = B )
3	1, 2	sylan2b 287	1 |- ( ( A = C /\ B = C ) -> A = B )

Syntax hints:   -> wi 4   /\ wa 104   = wceq 1373

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1470  ax-gen 1472  ax-4 1533  ax-17 1549  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-cleq 2198

This theorem is referenced by:  eueq  2944  euind  2960  reuind  2978  preqsn  3816  eusv1  4499  funopg  5305  funinsn  5323  foco  5509  funopdmsn  5764  mpofun  6047  enq0tr  7547  lteupri  7730  elrealeu  7942  rereceu  8002  receuap  8742  xrltso  9918  xrlttri3  9919  iseqf1olemab  10647  fsumparts  11781  odd2np1  12184  grpinveu  13370  exmidsbthrlem  15961