Theorem uneq2d 2184

Description: Deduction adding union to the left in a class equality.

Hypothesis

Ref	Expression
uneq1d.1	|- (ph -> A = B)

Assertion

Ref	Expression
uneq2d	|- (ph -> (C u. A) = (C u. B))

Proof of Theorem uneq2d

Step	Hyp	Ref	Expression
1		uneq1d.1	. 2 |- (ph -> A = B)
2		uneq2 2178	. 2 |- (A = B -> (C u. A) = (C u. B))
3	1, 2	syl 10	1 |- (ph -> (C u. A) = (C u. B))

Syntax hints:   -> wi 3   = wceq 956   u. cun 2045

This theorem is referenced by:  uneq12d 2185  suceq 3034  oev2 4162  oarec 4196  sbthlem5 4451  sbthlem6 4452  mapunen 4502  unifiOLD 4557  fiint 4559  fiintOLD 4560  fodomfiOLD 4566  pm54.43 4572  kmlem2 4766  kmlem11 4775  cdavalt 4919  icoun 6413  snunioo 6415  ioojoint 6416

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-un 2050

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