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Theorem unissd 3604
 Description: Subclass relationship for subclass union. Deduction form of uniss 3601. (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 3601 . 2 (𝐴𝐵 𝐴 𝐵)
31, 2syl 14 1 (𝜑 𝐴 𝐵)
 Colors of variables: wff set class Syntax hints:   → wi 4   ⊆ wss 2917  ∪ cuni 3580 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-in 2924  df-ss 2931  df-uni 3581 This theorem is referenced by:  iotanul  4882  tfrlemibfn  5942  tfrlemiubacc  5944
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