Theorem unieqi 3930

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 3929	. 2 |- ( A = B -> U. A = U. B )
3	1, 2	ax-mp 5	1 |- U. A = U. B

Syntax hints:   = wceq 1398   U.cuni 3920

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 2216

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-rex 2528  df-uni 3921

This theorem is referenced by:  elunirab  3933  unisn  3936  uniop  4378  unisuc  4540  unisucg  4541  univ  4603  dfiun3g  5020  op1sta  5250  op2nda  5253  dfdm2  5303  iotajust  5317  dfiota2  5319  cbviota  5323  cbviotavw  5324  sb8iota  5326  dffv4g  5673  funfvdm2f  5748  riotauni  6019  1st0  6352  2nd0  6353  unielxp  6382  brtpos0  6497  recsfval  6560  uniqs  6841  xpassen  7095  sup00  7308  suplocexprlemell  8045  uptx  15270