Theorem unieqi 3846

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 3845	. 2 |- ( A = B -> U. A = U. B )
3	1, 2	ax-mp 5	1 |- U. A = U. B

Syntax hints:   = wceq 1364   U.cuni 3836

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-rex 2478  df-uni 3837

This theorem is referenced by:  elunirab  3849  unisn  3852  uniop  4285  unisuc  4445  unisucg  4446  univ  4508  dfiun3g  4920  op1sta  5148  op2nda  5151  dfdm2  5201  iotajust  5215  dfiota2  5217  cbviota  5221  sb8iota  5223  dffv4g  5552  funfvdm2f  5623  riotauni  5881  1st0  6199  2nd0  6200  unielxp  6229  brtpos0  6307  recsfval  6370  uniqs  6649  xpassen  6886  sup00  7064  suplocexprlemell  7775  uptx  14453