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Theorem unssi 3178
 Description: An inference showing the union of two subclasses is a subclass. (Contributed by Raph Levien, 10-Dec-2002.)
Hypotheses
Ref Expression
unssi.1
unssi.2
Assertion
Ref Expression
unssi

Proof of Theorem unssi
StepHypRef Expression
1 unssi.1 . . 3
2 unssi.2 . . 3
31, 2pm3.2i 267 . 2
4 unss 3177 . 2
53, 4mpbi 144 1
 Colors of variables: wff set class Syntax hints:   wa 103   cun 3000   wss 3002 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2624  df-un 3006  df-in 3008  df-ss 3015 This theorem is referenced by:  undifabs  3365  inundifss  3366  dmrnssfld  4711  djuun  6816  caserel  6834  ltrelxr  7610  nn0ssre  8740  nn0ssz  8831  strleun  11646
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