Theorem uneq1i 3226

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 3223	. 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 1331   u. cun 3069

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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075

This theorem is referenced by:  un12  3234  unundi  3237  tpcoma  3617  qdass  3620  qdassr  3621  tpidm12  3622  resasplitss  5302  fmptpr  5612  df2o3  6327  undifdc  6812  sbthlemi6  6850  exmidfodomrlemim  7057  znnen  11911  setscom  11999