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Theorem poeq1 4216
 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 3926 . . . . . 6
21notbid 656 . . . . 5
3 breq 3926 . . . . . . 7
4 breq 3926 . . . . . . 7
53, 4anbi12d 464 . . . . . 6
6 breq 3926 . . . . . 6
75, 6imbi12d 233 . . . . 5
82, 7anbi12d 464 . . . 4
98ralbidv 2435 . . 3
1092ralbidv 2457 . 2
11 df-po 4213 . 2
12 df-po 4213 . 2
1310, 11, 123bitr4g 222 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   wb 104   wceq 1331  wral 2414   class class class wbr 3924   wpo 4211 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-in1 603  ax-in2 604  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-cleq 2130  df-clel 2133  df-ral 2419  df-br 3925  df-po 4213 This theorem is referenced by:  soeq1  4232
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