Theorem unieqi 3908

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 3907	. 2 |- ( A = B -> U. A = U. B )
3	1, 2	ax-mp 5	1 |- U. A = U. B

Syntax hints:   = wceq 1398   U.cuni 3898

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-rex 2517  df-uni 3899

This theorem is referenced by:  elunirab  3911  unisn  3914  uniop  4354  unisuc  4516  unisucg  4517  univ  4579  dfiun3g  4995  op1sta  5225  op2nda  5228  dfdm2  5278  iotajust  5292  dfiota2  5294  cbviota  5298  cbviotavw  5299  sb8iota  5301  dffv4g  5645  funfvdm2f  5720  riotauni  5988  1st0  6316  2nd0  6317  unielxp  6346  brtpos0  6461  recsfval  6524  uniqs  6805  xpassen  7057  sup00  7245  suplocexprlemell  7976  uptx  15065