Theorem uneq12 2179

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 2177	. 2 |- (A = B -> (A u. C) = (B u. C))
2		uneq2 2178	. 2 |- (C = D -> (B u. C) = (B u. D))
3	1, 2	sylan9eq 1527	1 |- ((A = B /\ C = D) -> (A u. C) = (B u. D))

Syntax hints:   -> wi 3   /\ wa 223   = wceq 956   u. cun 2045

This theorem is referenced by:  uneq12i 2182  un00 2306  opthprc 3221  unixp 3517  fnun 3594  oarec 4196  pm54.43 4572  trcl 4645

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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