Theorem ssun3 4190

Description: Subclass law for union of classes. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
ssun3	⊢ (𝐴 ⊆ 𝐵 → 𝐴 ⊆ (𝐵 ∪ 𝐶))

Proof of Theorem ssun3

Step	Hyp	Ref	Expression
1		ssun1 4188	. 2 ⊢ 𝐵 ⊆ (𝐵 ∪ 𝐶)
2		sstr2 4002	. 2 ⊢ (𝐴 ⊆ 𝐵 → (𝐵 ⊆ (𝐵 ∪ 𝐶) → 𝐴 ⊆ (𝐵 ∪ 𝐶)))
3	1, 2	mpi 20	1 ⊢ (𝐴 ⊆ 𝐵 → 𝐴 ⊆ (𝐵 ∪ 𝐶))

Syntax hints:   → wi 4   ∪ cun 3961   ⊆ wss 3963

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-un 3968  df-ss 3980

This theorem is referenced by:  ssun  4205  ssunsn2  4832  xpsspw  5822  wfrlem15OLD  8362  uncmp  23427  alexsubALTlem3  24073  sxbrsigalem0  34253  bnj1450  35043  fineqvac  35090  altxpsspw  35959  pibt2  37400  superuncl  43558  cnvtrcl0  43616