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Theorem unissd 3660
Description: Subclass relationship for subclass union. Deduction form of uniss 3657. (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 3657 . 2 (𝐴𝐵 𝐴 𝐵)
31, 2syl 14 1 (𝜑 𝐴 𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4  wss 2988   cuni 3636
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2617  df-in 2994  df-ss 3001  df-uni 3637
This theorem is referenced by:  iotanul  4958  tfrlemibfn  6041  tfrlemiubacc  6043  tfr1onlemssrecs  6052  tfr1onlembfn  6057  tfr1onlemubacc  6059  tfrcllemssrecs  6065  tfrcllembfn  6070  tfrcllemubacc  6072
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