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Theorem unieqd 3618
 Description: Deduction of equality of two class unions. (Contributed by NM, 21-Apr-1995.)
Hypothesis
Ref Expression
unieqd.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
unieqd (𝜑 𝐴 = 𝐵)

Proof of Theorem unieqd
StepHypRef Expression
1 unieqd.1 . 2 (𝜑𝐴 = 𝐵)
2 unieq 3616 . 2 (𝐴 = 𝐵 𝐴 = 𝐵)
31, 2syl 14 1 (𝜑 𝐴 = 𝐵)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1259  ∪ cuni 3607 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-uni 3608 This theorem is referenced by:  uniprg  3622  unisng  3624  unisn3  4207  onsucuni2  4315  opswapg  4834  elxp4  4835  elxp5  4836  iotaeq  4902  iotabi  4903  uniabio  4904  funfvdm  5263  funfvdm2  5264  fvun1  5266  fniunfv  5428  funiunfvdm  5429  1stvalg  5796  2ndvalg  5797  fo1st  5811  fo2nd  5812  f1stres  5813  f2ndres  5814  2nd1st  5833  cnvf1olem  5872  brtpos2  5896  dftpos4  5908  tpostpos  5909  recseq  5951  tfrexlem  5978  xpcomco  6330  xpassen  6334  xpdom2  6335  supeq1  6391  supeq2  6394  supeq3  6395  supeq123d  6396
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