Theorem uneq2 1606

Description: Equality theorem for the union of two classes.

Assertion

Ref	Expression
uneq2	|- (A = B -> (C u. A) = (C u. B))

Proof of Theorem uneq2

Step	Hyp	Ref	Expression
1		uneq1 1605	. 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	3eqtr4g 1147	1 |- (A = B -> (C u. A) = (C u. B))

Syntax hints:   -> wi 2   = wceq 1091   u. cun 1485

This theorem is referenced by:  uneq2i 1608  uneq2d 1611  uneq12 1613  unexb 1950  sucprc 2297  unxpdom 3650  sshjvalt 5321

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

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