Theorem uneq2i 3286

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 3283	. 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 3127

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 2739  df-un 3133

This theorem is referenced by:  un4  3295  unundir  3297  difun2  3502  difdifdirss  3507  qdass  3689  qdassr  3690  unisuc  4413  iunsuc  4420  fmptap  5706  fvsnun1  5713  rdgival  6382  rdg0  6387  undifdc  6922  exmidfodomrlemim  7199  djuassen  7215  facnn  10706  fac0  10707  fsum2dlemstep  11441  fsumiun  11484  fprod2dlemstep  11629