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Theorem unissd 3848
Description: Subclass relationship for subclass union. Deduction form of uniss 3845. (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 3845 . 2 (𝐴𝐵 𝐴 𝐵)
31, 2syl 14 1 (𝜑 𝐴 𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4  wss 3144   cuni 3824
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-in 3150  df-ss 3157  df-uni 3825
This theorem is referenced by:  iotanul  5211  tfrlemibfn  6353  tfrlemiubacc  6355  tfr1onlemssrecs  6364  tfr1onlembfn  6369  tfr1onlemubacc  6371  tfrcllemssrecs  6377  tfrcllembfn  6382  tfrcllemubacc  6384  fiuni  7007  eltg3i  14016  unitg  14022  tgss  14023  ntrss  14079
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