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Theorem supeq2 6876
 Description: Equality theorem for supremum. (Contributed by Jeff Madsen, 2-Sep-2009.)
Assertion
Ref Expression
supeq2

Proof of Theorem supeq2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 rabeq 2678 . . . 4
2 raleq 2626 . . . . . 6
32anbi2d 459 . . . . 5
43rabbidv 2675 . . . 4
51, 4eqtrd 2172 . . 3
65unieqd 3747 . 2
7 df-sup 6871 . 2
8 df-sup 6871 . 2
96, 7, 83eqtr4g 2197 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   wceq 1331  wral 2416  wrex 2417  crab 2420  cuni 3736   class class class wbr 3929  csup 6869 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-ral 2421  df-rex 2422  df-rab 2425  df-uni 3737  df-sup 6871 This theorem is referenced by:  infeq2  6901
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