Theorem unieqi 3611

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 3610	. 2 |- ( A = B -> U. A = U. B )
3	1, 2	ax-mp 7	1 |- U. A = U. B

Syntax hints:   = wceq 1284   U.cuni 3601

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-rex 2354  df-uni 3602

This theorem is referenced by:  elunirab  3614  unisn  3617  uniop  4010  unisuc  4168  unisucg  4169  univ  4225  dfiun3g  4607  op1sta  4822  op2nda  4825  dfdm2  4872  iotajust  4886  dfiota2  4888  cbviota  4892  sb8iota  4894  dffv4g  5195  funfvdm2f  5259  riotauni  5494  1st0  5791  2nd0  5792  unielxp  5820  brtpos0  5890  recsfval  5954  uniqs  6187  xpassen  6327  sup00  6416