Theorem uneq1i 3357

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 3354	. 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 1397   u. cun 3198

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-v 2804  df-un 3204

This theorem is referenced by:  un12  3365  unundi  3368  tpcoma  3765  qdass  3768  qdassr  3769  tpidm12  3770  resasplitss  5516  fmptpr  5845  df2o3  6596  undifdc  7115  sbthlemi6  7160  exmidfodomrlemim  7411  znnen  13018  setscom  13121