Theorem unissi 4860

Description: Subclass relationship for subclass union. Inference form of uniss 4859. (Contributed by David Moews, 1-May-2017.)

Hypothesis

Ref	Expression
unissi.1	⊢ 𝐴 ⊆ 𝐵

Assertion

Ref	Expression
unissi	⊢ ∪ 𝐴 ⊆ ∪ 𝐵

Proof of Theorem unissi

Step	Hyp	Ref	Expression
1		unissi.1	. 2 ⊢ 𝐴 ⊆ 𝐵
2		uniss 4859	. 2 ⊢ (𝐴 ⊆ 𝐵 → ∪ 𝐴 ⊆ ∪ 𝐵)
3	1, 2	ax-mp 5	1 ⊢ ∪ 𝐴 ⊆ ∪ 𝐵

Syntax hints:   ⊆ wss 3890  ∪ cuni 4851

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3432  df-ss 3907  df-uni 4852

This theorem is referenced by:  unidif  4886  unixpss  5760  riotassuni  7358  unifpw  9259  fiuni  9335  rankuni  9781  fin23lem29  10257  fin23lem30  10258  fin1a2lem12  10327  prdsds  17421  psss  18540  tgval2  22934  eltg4i  22938  ntrss2  23035  isopn3  23044  mretopd  23070  ordtbas  23170  cmpcov2  23368  tgcmp  23379  comppfsc  23510  alexsublem  24022  alexsubALTlem3  24027  alexsubALTlem4  24028  cldsubg  24089  bndth  24938  uniioombllem4  25566  uniioombllem5  25567  omssubadd  34463  cvmscld  35474  fnessref  36558  ttcuniun  36711  ttcuni  36714  inunissunidif  37708  mblfinlem3  37997  mblfinlem4  37998  ismblfin  37999  mbfresfi  38004  cover2  38053  salexct  46783  salgencntex  46792