Theorem uneq2 3329

Description: Equality theorem for the union of two classes. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem uneq2

Step	Hyp	Ref	Expression
1		uneq1 3328	. 2 |- ( A = B -> ( A u. C ) = ( B u. C ) )
2		uncom 3325	. 2 |- ( C u. A ) = ( A u. C )
3		uncom 3325	. 2 |- ( C u. B ) = ( B u. C )
4	1, 2, 3	3eqtr4g 2265	1 |- ( A = B -> ( C u. A ) = ( C u. B ) )

Syntax hints:   -> wi 4   = wceq 1373   u. cun 3172

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-v 2778  df-un 3178

This theorem is referenced by:  uneq12  3330  uneq2i  3332  uneq2d  3335  uneqin  3432  disjssun  3532  uniprg  3879  sucprc  4477  unexb  4507  unfiexmid  7041  unfidisj  7045  hashunlem  10986  bdunexb  16055  bj-unexg  16056