Theorem uneq2d 1611

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 1606	. 2 |- (A = B -> (C u. A) = (C u. B))
3	1, 2	syl 12	1 |- (ph -> (C u. A) = (C u. B))

Syntax hints:   -> wi 2   = wceq 1091   u. cun 1485

This theorem is referenced by:  uneq12d 1612  suceq 2288  tfrlem10 2958  sbthlem5 3353  sbthlem6 3354  mapunen 3397  fiint 3445  kmlem2 3581  kmlem10 3589  cdavalt 3716

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-un 1490

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