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Theorem uneq2 3412
 Description: Equality theorem for the union of two classes. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
uneq2 (A = B → (CA) = (CB))

Proof of Theorem uneq2
StepHypRef Expression
1 uneq1 3411 . 2 (A = B → (AC) = (BC))
2 uncom 3408 . 2 (CA) = (AC)
3 uncom 3408 . 2 (CB) = (BC)
41, 2, 33eqtr4g 2410 1 (A = B → (CA) = (CB))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642   ∪ cun 3207 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214 This theorem is referenced by:  uneq12  3413  uneq2i  3415  uneq2d  3418  uneqin  3506  disjssun  3608  uniprg  3906  eladdci  4399  addcid1  4405  elsuc  4413  addcass  4415  phialllem2  4617  cupvalg  5812
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