Theorem uneq2 2178

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 2177	. 2 |- (A = B -> (A u. C) = (B u. C))
2		uncom 2176	. 2 |- (C u. A) = (A u. C)
3		uncom 2176	. 2 |- (C u. B) = (B u. C)
4	1, 2, 3	3eqtr4g 1531	1 |- (A = B -> (C u. A) = (C u. B))

Syntax hints:   -> wi 3   = wceq 956   u. cun 2045

This theorem is referenced by:  uneq12 2179  uneq2i 2181  uneq2d 2184  uneqin 2256  uniprg 2516  unexb 2873  sucprc 3044  unxpdom 4844  sshjvalt 9320  spanunt 9468

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-un 2050

Copyright terms: Public domain