Theorem uneq2i 2181

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

Hypothesis

Ref	Expression
uneq1i.1	|- A = B

Assertion

Ref	Expression
uneq2i	|- (C u. A) = (C u. B)

Proof of Theorem uneq2i

Step	Hyp	Ref	Expression
1		uneq1i.1	. 2 |- A = B
2		uneq2 2178	. 2 |- (A = B -> (C u. A) = (C u. B))
3	1, 2	ax-mp 7	1 |- (C u. A) = (C u. B)

Syntax hints:   = wceq 956   u. cun 2045

This theorem is referenced by:  un23 2189  un4 2190  unundir 2192  difun2 2342  difdifdir 2346  unidif0 2739  unisuc 3046  onuninsuc 3108  fvsnun1 3795  fopabap 3841  tfrlem10 3920  oarec 4196  dfdom2 4384  fodomr 4483  unifiOLD 4557  ranksuc 4700  kmlem3 4767  cda0en 4925  xp2cda 4928  facnnt 6933  fac0 6934

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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