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Theorem uniprg 3751
 Description: The union of a pair is the union of its members. Proposition 5.7 of [TakeutiZaring] p. 16. (Contributed by NM, 25-Aug-2006.)
Assertion
Ref Expression
uniprg

Proof of Theorem uniprg
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 preq1 3600 . . . 4
21unieqd 3747 . . 3
3 uneq1 3223 . . 3
42, 3eqeq12d 2154 . 2
5 preq2 3601 . . . 4
65unieqd 3747 . . 3
7 uneq2 3224 . . 3
86, 7eqeq12d 2154 . 2
9 vex 2689 . . 3
10 vex 2689 . . 3
119, 10unipr 3750 . 2
124, 8, 11vtocl2g 2750 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1331   wcel 1480   cun 3069  cpr 3528  cuni 3736 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-uni 3737 This theorem is referenced by:  onun2  4406  unopn  12181
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