Theorem unieqi 3898

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 3897	. 2 |- ( A = B -> U. A = U. B )
3	1, 2	ax-mp 5	1 |- U. A = U. B

Syntax hints:   = wceq 1395   U.cuni 3888

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-rex 2514  df-uni 3889

This theorem is referenced by:  elunirab  3901  unisn  3904  uniop  4343  unisuc  4505  unisucg  4506  univ  4568  dfiun3g  4984  op1sta  5213  op2nda  5216  dfdm2  5266  iotajust  5280  dfiota2  5282  cbviota  5286  cbviotavw  5287  sb8iota  5289  dffv4g  5629  funfvdm2f  5704  riotauni  5970  1st0  6299  2nd0  6300  unielxp  6329  brtpos0  6409  recsfval  6472  uniqs  6753  xpassen  7002  sup00  7186  suplocexprlemell  7916  uptx  14969