Theorem elun2 2195

Description: Membership law for union of classes.

Assertion

Ref	Expression
elun2	|- (A e. B -> A e. (C u. B))

Proof of Theorem elun2

Step	Hyp	Ref	Expression
1		ssun2 2191	. 2 |- B (_ (C u. B)
2	1	sseli 2062	1 |- (A e. B -> A e. (C u. B))

Syntax hints:   -> wi 3   e. wcel 957   u. cun 2042

This theorem is referenced by:  tpi3 2454  tfrlem11 3916  rankun 4674  rankelun 4690  supxrun 6042  shslej 9293  cnfilca 10510

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-or 224  df-an 225  df-ex 980  df-sb 1171  df-clab 1463  df-cleq 1468  df-clel 1471  df-v 1809  df-un 2047  df-in 2048  df-ss 2050

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