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Theorem uneq2d 3418
 Description: Deduction adding union to the left in a class equality. (Contributed by NM, 29-Mar-1998.)
Hypothesis
Ref Expression
uneq1d.1 (φA = B)
Assertion
Ref Expression
uneq2d (φ → (CA) = (CB))

Proof of Theorem uneq2d
StepHypRef Expression
1 uneq1d.1 . 2 (φA = B)
2 uneq2 3412 . 2 (A = B → (CA) = (CB))
31, 2syl 15 1 (φ → (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:  ifeq2  3667  tpeq3  3810  iununi  4050  prprc2  4122  pw1eqadj  4332  elsuci  4414  nnsucelr  4428  nnadjoin  4520  opeq2  4579  fvun1  5379  fvunsn  5444  enadj  6060  nmembers1lem3  6270  frecxp  6314
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