Theorem uneq2i 3174

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 3171	. 2 |- ( A = B -> ( C u. A ) = ( C u. B ) )
3	1, 2	ax-mp 7	1 |- ( C u. A ) = ( C u. B )

Syntax hints:   = wceq 1299   u. cun 3019

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082

This theorem depends on definitions:  df-bi 116  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-v 2643  df-un 3025

This theorem is referenced by:  un4  3183  unundir  3185  difun2  3389  difdifdirss  3394  qdass  3567  qdassr  3568  unisuc  4273  iunsuc  4280  fmptap  5542  fvsnun1  5549  rdgival  6209  rdg0  6214  undifdc  6741  exmidfodomrlemim  6966  djuassen  6977  facnn  10314  fac0  10315  fsum2dlemstep  11042  fsumiun  11085