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Theorem unissi 3759
 Description: Subclass relationship for subclass union. Inference form of uniss 3757. (Contributed by David Moews, 1-May-2017.)
Hypothesis
Ref Expression
unissi.1 𝐴𝐵
Assertion
Ref Expression
unissi 𝐴 𝐵

Proof of Theorem unissi
StepHypRef Expression
1 unissi.1 . 2 𝐴𝐵
2 uniss 3757 . 2 (𝐴𝐵 𝐴 𝐵)
31, 2ax-mp 5 1 𝐴 𝐵
 Colors of variables: wff set class Syntax hints:   ⊆ wss 3071  ∪ cuni 3736 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-in 3077  df-ss 3084  df-uni 3737 This theorem is referenced by:  unidif  3768  unixpss  4652  tfrcllemssrecs  6249  tgvalex  12229  tgval2  12230  eltg4i  12234  ntrss2  12300  isopn3  12304
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