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Theorem elun1 3138
Description: Membership law for union of classes. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
elun1  |-  ( A  e.  B  ->  A  e.  ( B  u.  C
) )

Proof of Theorem elun1
StepHypRef Expression
1 ssun1 3134 . 2  |-  B  C_  ( B  u.  C
)
21sseli 2969 1  |-  ( A  e.  B  ->  A  e.  ( B  u.  C
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1409    u. cun 2943
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-in 2952  df-ss 2959
This theorem is referenced by:  brtposg  5900  dftpos4  5909  nndifsnid  6111  fidifsnid  6363
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