Theorem ssun3 4109

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 4107	. 2 ⊢ 𝐵 ⊆ (𝐵 ∪ 𝐶)
2		sstr2 3922	. 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 3881   ⊆ wss 3883

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-v 3433  df-un 3888  df-ss 3900

This theorem is referenced by:  ssun  4124  ssunsn2  4758  xpsspw  5752  uncmp  23386  alexsubALTlem3  24032  constrextdg2lem  33932  sxbrsigalem0  34455  bnj1450  35232  fineqvac  35297  altxpsspw  36205  ttcuniun  36738  ttciunun  36739  pibt2  37779  superuncl  44012  cnvtrcl0  44070