Theorem elun2 1626

Description: Membership law for union of classes.

Assertion

Ref	Expression
elun2	⊢ (A ∈ B → A ∈ (C ∪ B))

Proof of Theorem elun2

Step	Hyp	Ref	Expression
1		ssun2 1622	. 2 ⊢ B ⊆ (C ∪ B)
2	1	sseli 1504	1 ⊢ (A ∈ B → A ∈ (C ∪ B))

Syntax hints:   → wi 2   ∈ wcel 1092   ∪ cun 1485

This theorem is referenced by:  tpi3 1845  tfrlem11 2959  rankun 3535  shslej 5339

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-un 1490  df-in 1491  df-ss 1492

metamath.org