Theorem ssun2 3204

Description: Subclass relationship for union of classes. (Contributed by NM, 30-Aug-1993.)

Assertion

Ref	Expression
ssun2	⊢ 𝐴 ⊆ (𝐵 ∪ 𝐴)

Proof of Theorem ssun2

Step	Hyp	Ref	Expression
1		ssun1 3203	. 2 ⊢ 𝐴 ⊆ (𝐴 ∪ 𝐵)
2		uncom 3184	. 2 ⊢ (𝐴 ∪ 𝐵) = (𝐵 ∪ 𝐴)
3	1, 2	sseqtri 3095	1 ⊢ 𝐴 ⊆ (𝐵 ∪ 𝐴)

Syntax hints:   ∪ cun 3033   ⊆ wss 3035

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1404  ax-7 1405  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-10 1464  ax-11 1465  ax-i12 1466  ax-bndl 1467  ax-4 1468  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-i5r 1496  ax-ext 2095

This theorem depends on definitions:  df-bi 116  df-tru 1315  df-nf 1418  df-sb 1717  df-clab 2100  df-cleq 2106  df-clel 2109  df-nfc 2242  df-v 2657  df-un 3039  df-in 3041  df-ss 3048

This theorem is referenced by:  ssun4  3206  elun2  3208  unv  3364  un00  3373  snsspr2  3633  snsstp3  3636  unexb  4321  rnexg  4760  brtpos0  6101  ac6sfi  6743  caserel  6922  pnfxr  7736  ltrelxr  7743  un0mulcl  8909  fsumsplit  11062  bdunexb  12801