Theorem unieqi 3923

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 3922	. 2 |- ( A = B -> U. A = U. B )
3	1, 2	ax-mp 5	1 |- U. A = U. B

Syntax hints:   = wceq 1398   U.cuni 3913

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 2214

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-rex 2526  df-uni 3914

This theorem is referenced by:  elunirab  3926  unisn  3929  uniop  4371  unisuc  4533  unisucg  4534  univ  4596  dfiun3g  5013  op1sta  5243  op2nda  5246  dfdm2  5296  iotajust  5310  dfiota2  5312  cbviota  5316  cbviotavw  5317  sb8iota  5319  dffv4g  5666  funfvdm2f  5741  riotauni  6009  1st0  6337  2nd0  6338  unielxp  6367  brtpos0  6482  recsfval  6545  uniqs  6826  xpassen  7080  sup00  7293  suplocexprlemell  8027  uptx  15131