Theorem uneq2i 3288

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

Hypothesis

Ref	Expression
uneq1i.1	|- A = B

Assertion

Ref	Expression
uneq2i	|- ( C u. A ) = ( C u. B )

Proof of Theorem uneq2i

Step	Hyp	Ref	Expression
1		uneq1i.1	. 2 |- A = B
2		uneq2 3285	. 2 |- ( A = B -> ( C u. A ) = ( C u. B ) )
3	1, 2	ax-mp 5	1 |- ( C u. A ) = ( C u. B )

Syntax hints:   = wceq 1353   u. cun 3129

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2741  df-un 3135

This theorem is referenced by:  un4  3297  unundir  3299  difun2  3504  difdifdirss  3509  qdass  3691  qdassr  3692  unisuc  4415  iunsuc  4422  fmptap  5708  fvsnun1  5715  rdgival  6385  rdg0  6390  undifdc  6925  exmidfodomrlemim  7202  djuassen  7218  facnn  10709  fac0  10710  fsum2dlemstep  11444  fsumiun  11487  fprod2dlemstep  11632