Theorem uniiun 2597

Description: Class union in terms of indexed union. Definition of [Stoll] p. 43.

Assertion

Ref	Expression
uniiun	|- U.A = U_x e. A x

Distinct variable group:   x,A

Proof of Theorem uniiun

Step	Hyp	Ref	Expression
1		dfuni2 2501	. 2 |- U.A = {y | E.x e. A y e. x}
2		df-iun 2564	. 2 |- U_x e. A x = {y | E.x e. A y e. x}
3	1, 2	eqtr4 1496	1 |- U.A = U_x e. A x

Syntax hints:   = wceq 955   e. wcel 957  {cab 1462  E.wrex 1644  U.cuni 2499  U_ciun 2562

This theorem is referenced by:  iunpwss 2614  iunpw 2910  oa0r 4166  om1r 4170  oeworde 4213  oaabs 4245  unictb 7536  subtop 7606

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-12 967  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  ax-16 1209  ax-11o 1217  ax-ext 1458

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 980  df-sb 1171  df-clab 1463  df-cleq 1468  df-clel 1471  df-rex 1648  df-uni 2500  df-iun 2564

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