Theorem uneq2i 3355

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 3352	. 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 1395   u. cun 3195

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-un 3201

This theorem is referenced by:  un4  3364  unundir  3366  difun2  3571  difdifdirss  3576  qdass  3763  qdassr  3764  unisuc  4504  iunsuc  4511  fmptap  5829  fvsnun1  5836  rdgival  6528  rdg0  6533  undifdc  7086  exmidfodomrlemim  7379  djuassen  7399  facnn  10949  fac0  10950  fsum2dlemstep  11945  fsumiun  11988  fprod2dlemstep  12133  plyun0  15410  lgsquadlem3  15758