Theorem uneq2i 3324

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 3321	. 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 1373   u. cun 3164

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-un 3170

This theorem is referenced by:  un4  3333  unundir  3335  difun2  3540  difdifdirss  3545  qdass  3730  qdassr  3731  unisuc  4461  iunsuc  4468  fmptap  5776  fvsnun1  5783  rdgival  6470  rdg0  6475  undifdc  7023  exmidfodomrlemim  7311  djuassen  7331  facnn  10874  fac0  10875  fsum2dlemstep  11778  fsumiun  11821  fprod2dlemstep  11966  plyun0  15241  lgsquadlem3  15589