Theorem uneq1i 3272

Description: Inference adding union to the right in a class equality. (Contributed by NM, 30-Aug-1993.)

Hypothesis

Ref	Expression
uneq1i.1	|- A = B

Assertion

Ref	Expression
uneq1i	|- ( A u. C ) = ( B u. C )

Proof of Theorem uneq1i

Step	Hyp	Ref	Expression
1		uneq1i.1	. 2 |- A = B
2		uneq1 3269	. 2 |- ( A = B -> ( A u. C ) = ( B u. C ) )
3	1, 2	ax-mp 5	1 |- ( A u. C ) = ( B u. C )

Syntax hints:   = wceq 1343   u. cun 3114

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 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-v 2728  df-un 3120

This theorem is referenced by:  un12  3280  unundi  3283  tpcoma  3670  qdass  3673  qdassr  3674  tpidm12  3675  resasplitss  5367  fmptpr  5677  df2o3  6398  undifdc  6889  sbthlemi6  6927  exmidfodomrlemim  7157  znnen  12331  setscom  12434