Theorem unieqi 3849

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 3848	. 2 |- ( A = B -> U. A = U. B )
3	1, 2	ax-mp 5	1 |- U. A = U. B

Syntax hints:   = wceq 1364   U.cuni 3839

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-rex 2481  df-uni 3840

This theorem is referenced by:  elunirab  3852  unisn  3855  uniop  4288  unisuc  4448  unisucg  4449  univ  4511  dfiun3g  4923  op1sta  5151  op2nda  5154  dfdm2  5204  iotajust  5218  dfiota2  5220  cbviota  5224  sb8iota  5226  dffv4g  5555  funfvdm2f  5626  riotauni  5884  1st0  6202  2nd0  6203  unielxp  6232  brtpos0  6310  recsfval  6373  uniqs  6652  xpassen  6889  sup00  7069  suplocexprlemell  7780  uptx  14510