Theorem uneq1i 1607

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

Hypothesis

Ref	Expression
uneq1i.1	|- A = B

Assertion

Ref	Expression
uneq1i	|- (A u. C) = (B u. C)

Proof of Theorem uneq1i

Step	Hyp	Ref	Expression
1		uneq1i.1	. 2 |- A = B
2		uneq1 1605	. 2 |- (A = B -> (A u. C) = (B u. C))
3	1, 2	ax-mp 6	1 |- (A u. C) = (B u. C)

Syntax hints:   = wceq 1091   u. cun 1485

This theorem is referenced by:  uneq12i 1609  un12 1616  unundi 1619  undif1 1761  unidif0 1944  sbthlem6 3354  kmlem10 3589  fodomb 3615

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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