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Theorem uniss 3725
 Description: Subclass relationship for class union. Theorem 61 of [Suppes] p. 39. (Contributed by NM, 22-Mar-1998.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
uniss

Proof of Theorem uniss
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ssel 3059 . . . . 5
21anim2d 333 . . . 4
32eximdv 1834 . . 3
4 eluni 3707 . . 3
5 eluni 3707 . . 3
63, 4, 53imtr4g 204 . 2
76ssrdv 3071 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103  wex 1451   wcel 1463   wss 3039  cuni 3704 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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-in 3045  df-ss 3052  df-uni 3705 This theorem is referenced by:  unissi  3727  unissd  3728  intssuni2m  3763  relfld  5035  tgcl  12128  distop  12149
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