Theorem unss2 1629

Description: Subclass law for union of classes. Exercise 7 of [TakeutiZaring] p. 18.

Assertion

Ref	Expression
unss2	|- (A (_ B -> (C u. A) (_ (C u. B))

Proof of Theorem unss2

Step	Hyp	Ref	Expression
1		unss1 1627	. 2 |- (A (_ B -> (A u. C) (_ (B u. C))
2		uncom 1604	. 2 |- (C u. A) = (A u. C)
3		uncom 1604	. 2 |- (C u. B) = (B u. C)
4	1, 2, 3	3sstr4g 1541	1 |- (A (_ B -> (C u. A) (_ (C u. B))

Syntax hints:   -> wi 2   u. cun 1485   (_ wss 1487

This theorem is referenced by:  unss12 1630

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

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