Theorem unieqi 3590

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 3589	. 2 |- ( A = B -> U. A = U. B )
3	1, 2	ax-mp 7	1 |- U. A = U. B

Syntax hints:   = wceq 1243   U.cuni 3580

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-uni 3581

This theorem is referenced by:  elunirab  3593  unisn  3596  uniop  3992  unisuc  4150  unisucg  4151  univ  4207  dfiun3g  4589  op1sta  4802  op2nda  4805  dfdm2  4852  iotajust  4866  dfiota2  4868  cbviota  4872  sb8iota  4874  dffv4g  5175  funfvdm2f  5238  riotauni  5474  1st0  5771  2nd0  5772  unielxp  5800  brtpos0  5867  recsfval  5931  uniqs  6164  xpassen  6304