Theorem uneq12 2231

Description: Equality theorem for union of two classes.

Assertion

Ref	Expression
uneq12	|- ((A = B /\ C = D) -> (A u. C) = (B u. D))

Proof of Theorem uneq12

Step	Hyp	Ref	Expression
1		uneq1 2229	. 2 |- (A = B -> (A u. C) = (B u. C))
2		uneq2 2230	. 2 |- (C = D -> (B u. C) = (B u. D))
3	1, 2	sylan9eq 1570	1 |- ((A = B /\ C = D) -> (A u. C) = (B u. D))

Syntax hints:   -> wi 3   /\ wa 221   = wceq 992   u. cun 2097

This theorem is referenced by:  uneq12i 2234  un00 2359  opthprc 3306  unixp 3622  fnun 3700  oarec 4332  pm54.43 4715  trcl 4791  elfiun 11421

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 998  ax-gen 999  ax-8 1000  ax-10 1002  ax-12 1004  ax-17 1007  ax-4 1009  ax-5o 1011  ax-6o 1014  ax-9o 1159  ax-10o 1177  ax-16 1247  ax-11o 1255  ax-ext 1500

This theorem depends on definitions:  df-bi 145  df-or 222  df-an 223  df-ex 1017  df-sb 1209  df-clab 1506  df-cleq 1511  df-clel 1514  df-v 1858  df-un 2102

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