Theorem unissi 3872

Description: Subclass relationship for subclass union. Inference form of uniss 3870. (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 3870	. 2 ⊢ (𝐴 ⊆ 𝐵 → ∪ 𝐴 ⊆ ∪ 𝐵)
3	1, 2	ax-mp 5	1 ⊢ ∪ 𝐴 ⊆ ∪ 𝐵

Syntax hints:   ⊆ wss 3165  ∪ cuni 3849

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 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186

This theorem depends on definitions:  df-bi 117  df-tru 1375  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-nfc 2336  df-v 2773  df-in 3171  df-ss 3178  df-uni 3850

This theorem is referenced by:  unidif  3881  unixpss  4786  tfrcllemssrecs  6428  tgvalex  13013  tgval2  14441  eltg4i  14445  ntrss2  14511  isopn3  14515