Theorem uneq2 3229

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 3228	. 2 |- ( A = B -> ( A u. C ) = ( B u. C ) )
2		uncom 3225	. 2 |- ( C u. A ) = ( A u. C )
3		uncom 3225	. 2 |- ( C u. B ) = ( B u. C )
4	1, 2, 3	3eqtr4g 2198	1 |- ( A = B -> ( C u. A ) = ( C u. B ) )

Syntax hints:   -> wi 4   = wceq 1332   u. cun 3074

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-un 3080

This theorem is referenced by:  uneq12  3230  uneq2i  3232  uneq2d  3235  uneqin  3332  disjssun  3431  uniprg  3759  sucprc  4342  unexb  4371  unfiexmid  6814  unfidisj  6818  hashunlem  10582  bdunexb  13289  bj-unexg  13290