Theorem uneq2d 2174

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 2168	. 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 953   u. cun 2035

This theorem is referenced by:  uneq12d 2175  suceq 3024  oev2 4146  oarec 4180  sbthlem5 4431  sbthlem6 4432  mapunen 4482  unifi 4532  fiint 4534  fodomfi 4540  pm54.43 4546  kmlem2 4738  kmlem11 4747  cdavalt 4891  icoun 6346  snunioo 6348

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-v 1803  df-un 2040

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