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Theorem unieqi 3714
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 3713 . 2 (𝐴 = 𝐵 𝐴 = 𝐵)
31, 2ax-mp 5 1 𝐴 = 𝐵
Colors of variables: wff set class
Syntax hints:   = wceq 1314   cuni 3704
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-rex 2397  df-uni 3705
This theorem is referenced by:  elunirab  3717  unisn  3720  uniop  4145  unisuc  4303  unisucg  4304  univ  4365  dfiun3g  4764  op1sta  4988  op2nda  4991  dfdm2  5041  iotajust  5055  dfiota2  5057  cbviota  5061  sb8iota  5063  dffv4g  5384  funfvdm2f  5452  riotauni  5702  1st0  6008  2nd0  6009  unielxp  6038  brtpos0  6115  recsfval  6178  uniqs  6453  xpassen  6690  sup00  6856  suplocexprlemell  7485  uptx  12349
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