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Theorem unissd 3683
Description: Subclass relationship for subclass union. Deduction form of uniss 3680. (Contributed by David Moews, 1-May-2017.)
Hypothesis
Ref Expression
unissd.1 (𝜑𝐴𝐵)
Assertion
Ref Expression
unissd (𝜑 𝐴 𝐵)

Proof of Theorem unissd
StepHypRef Expression
1 unissd.1 . 2 (𝜑𝐴𝐵)
2 uniss 3680 . 2 (𝐴𝐵 𝐴 𝐵)
31, 2syl 14 1 (𝜑 𝐴 𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4  wss 3000   cuni 3659
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 2622  df-in 3006  df-ss 3013  df-uni 3660
This theorem is referenced by:  iotanul  5008  tfrlemibfn  6107  tfrlemiubacc  6109  tfr1onlemssrecs  6118  tfr1onlembfn  6123  tfr1onlemubacc  6125  tfrcllemssrecs  6131  tfrcllembfn  6136  tfrcllemubacc  6138  eltg3i  11810  unitg  11816  tgss  11817  ntrss  11873
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