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Theorem poeq1 4809
 Description: Equality theorem for partial ordering predicate. (Contributed by NM, 27-Mar-1997.)
Assertion
Ref Expression
poeq1

Proof of Theorem poeq1
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 breq 4455 . . . . . 6
21notbid 294 . . . . 5
3 breq 4455 . . . . . . 7
4 breq 4455 . . . . . . 7
53, 4anbi12d 710 . . . . . 6
6 breq 4455 . . . . . 6
75, 6imbi12d 320 . . . . 5
82, 7anbi12d 710 . . . 4
98ralbidv 2906 . . 3
1092ralbidv 2911 . 2
11 df-po 4806 . 2
12 df-po 4806 . 2
1310, 11, 123bitr4g 288 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184   wa 369   wceq 1379  wral 2817   class class class wbr 4453   wpo 4804 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1597  df-cleq 2459  df-clel 2462  df-ral 2822  df-br 4454  df-po 4806 This theorem is referenced by:  soeq1  4825
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