Theorem uneq1i 2183

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 2180	. 2 |- (A = B -> (A u. C) = (B u. C))
3	1, 2	ax-mp 7	1 |- (A u. C) = (B u. C)

Syntax hints:   = wceq 958   u. cun 2048

This theorem is referenced by:  un12 2191  unundi 2194  undif1 2344  unidif0 2744  sbthlem6 4458  fodomr 4489  kmlem11 4785

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-v 1815  df-un 2053

Copyright terms: Public domain