Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  weeq2 Unicode version

Theorem weeq2 4094
 Description: Equality theorem for the well-ordering predicate. (Contributed by NM, 3-Apr-1994.)
Assertion
Ref Expression
weeq2

Proof of Theorem weeq2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 freq2 4083 . . 3
2 raleq 2505 . . . . 5
32raleqbi1dv 2513 . . . 4
43raleqbi1dv 2513 . . 3
51, 4anbi12d 442 . 2
6 df-wetr 4071 . 2
7 df-wetr 4071 . 2
85, 6, 73bitr4g 212 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1243  wral 2306   class class class wbr 3764   wfr 4065   wwe 4067 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-in 2924  df-ss 2931  df-frfor 4068  df-frind 4069  df-wetr 4071 This theorem is referenced by:  reg3exmid  4304
 Copyright terms: Public domain W3C validator