Theorem unieqi 3820

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 3819	. 2 |- ( A = B -> U. A = U. B )
3	1, 2	ax-mp 5	1 |- U. A = U. B

Syntax hints:   = wceq 1353   U.cuni 3810

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rex 2461  df-uni 3811

This theorem is referenced by:  elunirab  3823  unisn  3826  uniop  4256  unisuc  4414  unisucg  4415  univ  4477  dfiun3g  4885  op1sta  5111  op2nda  5114  dfdm2  5164  iotajust  5178  dfiota2  5180  cbviota  5184  sb8iota  5186  dffv4g  5513  funfvdm2f  5582  riotauni  5837  1st0  6145  2nd0  6146  unielxp  6175  brtpos0  6253  recsfval  6316  uniqs  6593  xpassen  6830  sup00  7002  suplocexprlemell  7712  uptx  13777