Theorem unissi 3830

Description: Subclass relationship for subclass union. Inference form of uniss 3828. (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 3828	. 2 ⊢ (𝐴 ⊆ 𝐵 → ∪ 𝐴 ⊆ ∪ 𝐵)
3	1, 2	ax-mp 5	1 ⊢ ∪ 𝐴 ⊆ ∪ 𝐵

Syntax hints:   ⊆ wss 3129  ∪ cuni 3807

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-in 3135  df-ss 3142  df-uni 3808

This theorem is referenced by:  unidif  3839  unixpss  4735  tfrcllemssrecs  6346  tgvalex  13183  tgval2  13184  eltg4i  13188  ntrss2  13254  isopn3  13258