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Theorem uneq12 3086
Description: Equality theorem for union of two classes. (Contributed by NM, 29-Mar-1998.)
Assertion
Ref Expression
uneq12 ((A = B 𝐶 = 𝐷) → (A𝐶) = (B𝐷))

Proof of Theorem uneq12
StepHypRef Expression
1 uneq1 3084 . 2 (A = B → (A𝐶) = (B𝐶))
2 uneq2 3085 . 2 (𝐶 = 𝐷 → (B𝐶) = (B𝐷))
31, 2sylan9eq 2089 1 ((A = B 𝐶 = 𝐷) → (A𝐶) = (B𝐷))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   = wceq 1242  cun 2909
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916
This theorem is referenced by:  uneq12i  3089  uneq12d  3092  un00  3257  opthprc  4334  dmpropg  4736  unixpm  4796  fntpg  4898  fnun  4948  resasplitss  5012
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