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Theorem unieqi 3617
 Description: Inference of equality of two class unions. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
unieqi.1 𝐴 = 𝐵
Assertion
Ref Expression
unieqi 𝐴 = 𝐵

Proof of Theorem unieqi
StepHypRef Expression
1 unieqi.1 . 2 𝐴 = 𝐵
2 unieq 3616 . 2 (𝐴 = 𝐵 𝐴 = 𝐵)
31, 2ax-mp 7 1 𝐴 = 𝐵
 Colors of variables: wff set class Syntax hints:   = 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:  elunirab  3620  unisn  3623  uniop  4019  unisuc  4177  unisucg  4178  univ  4234  dfiun3g  4616  op1sta  4829  op2nda  4832  dfdm2  4879  iotajust  4893  dfiota2  4895  cbviota  4899  sb8iota  4901  dffv4g  5202  funfvdm2f  5265  riotauni  5501  1st0  5798  2nd0  5799  unielxp  5827  brtpos0  5897  recsfval  5961  uniqs  6194  xpassen  6334  sup00  6406
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