Theorem unieqi 3754

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 3753	. 2 |- ( A = B -> U. A = U. B )
3	1, 2	ax-mp 5	1 |- U. A = U. B

Syntax hints:   = wceq 1332   U.cuni 3744

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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-uni 3745

This theorem is referenced by:  elunirab  3757  unisn  3760  uniop  4185  unisuc  4343  unisucg  4344  univ  4405  dfiun3g  4804  op1sta  5028  op2nda  5031  dfdm2  5081  iotajust  5095  dfiota2  5097  cbviota  5101  sb8iota  5103  dffv4g  5426  funfvdm2f  5494  riotauni  5744  1st0  6050  2nd0  6051  unielxp  6080  brtpos0  6157  recsfval  6220  uniqs  6495  xpassen  6732  sup00  6898  suplocexprlemell  7545  uptx  12482