Theorem uneq1i 3304

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 3301	. 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 1364   u. cun 3146

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2758  df-un 3152

This theorem is referenced by:  un12  3312  unundi  3315  tpcoma  3708  qdass  3711  qdassr  3712  tpidm12  3713  resasplitss  5421  fmptpr  5736  df2o3  6463  undifdc  6960  sbthlemi6  7000  exmidfodomrlemim  7240  znnen  12466  setscom  12569