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Theorem uneq1i 3414
Description: Inference adding union to the right in a class equality. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
uneq1i.1 A = B
Assertion
Ref Expression
uneq1i (AC) = (BC)

Proof of Theorem uneq1i
StepHypRef Expression
1 uneq1i.1 . 2 A = B
2 uneq1 3411 . 2 (A = B → (AC) = (BC))
31, 2ax-mp 8 1 (AC) = (BC)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1642  cun 3207
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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:  un12  3421  unundi  3424  undif1  3625  dfif5  3674  tpcoma  3816  qdass  3819  qdassr  3820  tpidm12  3821  nnsucelrlem3  4426  phialllem2  4617  sbthlem1  6203  addccan2nclem2  6264
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