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Theorem weeq1 4119
 Description: Equality theorem for the well-ordering predicate. (Contributed by NM, 9-Mar-1997.)
Assertion
Ref Expression
weeq1

Proof of Theorem weeq1
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 freq1 4107 . . 3
2 breq 3795 . . . . . . . 8
3 breq 3795 . . . . . . . 8
42, 3anbi12d 457 . . . . . . 7
5 breq 3795 . . . . . . 7
64, 5imbi12d 232 . . . . . 6
76ralbidv 2369 . . . . 5
87ralbidv 2369 . . . 4
98ralbidv 2369 . . 3
101, 9anbi12d 457 . 2
11 df-wetr 4097 . 2
12 df-wetr 4097 . 2
1310, 11, 123bitr4g 221 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103   wceq 1285  wral 2349   class class class wbr 3793   wfr 4091   wwe 4093 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-cleq 2075  df-clel 2078  df-ral 2354  df-br 3794  df-frfor 4094  df-frind 4095  df-wetr 4097 This theorem is referenced by: (None)
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