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Theorem unssi 3118
 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 257 . 2
4 unss 3117 . 2
53, 4mpbi 133 1
 Colors of variables: wff set class Syntax hints:   wa 97   cun 2915   wss 2917 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931 This theorem is referenced by:  undifabs  3300  inundifss  3301  dmrnssfld  4595  ltrelxr  7080  nn0ssre  8185  nn0ssz  8263
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