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Theorem dfiun2 3685
Description: Alternate definition of indexed union when B is a set. Definition 15(a) of [Suppes] p. 44. (Contributed by NM, 27-Jun-1998.) (Revised by David Abernethy, 19-Jun-2012.)
Hypothesis
Ref Expression
dfiun2.1 B V
Assertion
Ref Expression
dfiun2 x A B = {yx A y = B}
Distinct variable groups:   x,y   y,A   y,B
Allowed substitution hints:   A(x)   B(x)

Proof of Theorem dfiun2
StepHypRef Expression
1 dfiun2g 3683 . 2 (x A B V → x A B = {yx A y = B})
2 dfiun2.1 . . 3 B V
32a1i 9 . 2 (x AB V)
41, 3mprg 2375 1 x A B = {yx A y = B}
Colors of variables: wff set class
Syntax hints:   = wceq 1243   wcel 1393  {cab 2026  wrex 2304  Vcvv 2554   cuni 3574   ciun 3651
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-ral 2308  df-rex 2309  df-v 2556  df-uni 3575  df-iun 3653
This theorem is referenced by:  funcnvuni  4914  fun11iun  5093  tfrlem8  5879
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