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Theorem supeq2 7456
 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 2952 . . . 4
2 raleq 2906 . . . . . 6
32anbi2d 686 . . . . 5
43rabbidv 2950 . . . 4
51, 4eqtrd 2470 . . 3
65unieqd 4028 . 2
7 df-sup 7449 . 2
8 df-sup 7449 . 2
96, 7, 83eqtr4g 2495 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360   wceq 1653  wral 2707  wrex 2708  crab 2711  cuni 4017   class class class wbr 4215  csup 7448 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-uni 4018  df-sup 7449
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