Theorem unieqi 3746

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	|- U. A = U. B

Proof of Theorem unieqi

Step	Hyp	Ref	Expression
1		unieqi.1	. 2 |- A = B
2		unieq 3745	. 2 |- ( A = B -> U. A = U. B )
3	1, 2	ax-mp 5	1 |- U. A = U. B

Syntax hints:   = wceq 1331   U.cuni 3736

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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-uni 3737

This theorem is referenced by:  elunirab  3749  unisn  3752  uniop  4177  unisuc  4335  unisucg  4336  univ  4397  dfiun3g  4796  op1sta  5020  op2nda  5023  dfdm2  5073  iotajust  5087  dfiota2  5089  cbviota  5093  sb8iota  5095  dffv4g  5418  funfvdm2f  5486  riotauni  5736  1st0  6042  2nd0  6043  unielxp  6072  brtpos0  6149  recsfval  6212  uniqs  6487  xpassen  6724  sup00  6890  suplocexprlemell  7521  uptx  12443