Theorem uneq1d 2183

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

Hypothesis

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

Assertion

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

Proof of Theorem uneq1d

Step	Hyp	Ref	Expression
1		uneq1d.1	. 2 |- (ph -> A = B)
2		uneq1 2177	. 2 |- (A = B -> (A u. C) = (B u. C))
3	1, 2	syl 10	1 |- (ph -> (A u. C) = (B u. C))

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

This theorem is referenced by:  uneq12d 2185  preq1 2448  sbthlem5 4451  fodomr 4483  mapunen 4502  cdavalt 4919  icoun 6413

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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